Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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Chapter 10.5, Problem 4E
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538 Chapter 13
12. Given: Points E(-4, 1), F(2, 3), G(4, 9), and H(-2, 7)
a. Show that EFGH is a rhombus.
b. Use slopes to verify that the diagonals are
perpendicular.
13. Given: Points R(-4, 5), S(-1, 9), T(7, 3) and U(4, -1)
a. Show that RSTU is a rectangle.
b. Use the distance formula to verify that the diagonals are congruent.
14. Given: Points N(-1, -5), O(0, 0), P(3, 2), and 2(8, 1)
a. Show that NOPQ is an isosceles trapezoid.
b. Show that the diagonals are congruent.
Decide what special type of quadrilateral HIJK is. Then prove that your
answer is correct.
15. H(0, 0)
16. H(0, 1)
17. H(7, 5)
18. H(-3, -3)
I(5, 0)
I(2,-3)
1(8, 3)
I(-5, -6)
J(7, 9)
K(1, 9)
J(-2, -1)
K(-4, 3)
J(0, -1)
K(-1, 1)
J(4, -5)
K(6,-2)
19. Point N(3, - 4) lies on the circle x² +
y² = 25. What is the slope of the
(Hint: Recall Theorem 9-1.)
-
line that is tangent to the circle at N?
20. Point P(6, 7) lies on the circle (x + 2)² + (y − 1)² = 100. What is the
slope of the line that is tangent to the circle at…
Can you cut the 12 glass triangles from a sheet of glass that is 4 feet by 8 feet? If so, how can it be done?
Can you cut 12 glass triangles from a sheet of glass that is 4 feet by 8 feet? If so, draw a diagram of how it can be done.
Chapter 10 Solutions
Elementary Geometry For College Students, 7e
Ch. 10.1 - Plot and then label the points A0,-3, B3,-4, C5,...Ch. 10.1 - Give the coordinates of each point A, B, C, D, and...Ch. 10.1 - Find the distance between each pair of points: a...Ch. 10.1 - If the distance between -2, 3 and -2,a is 5 units,...Ch. 10.1 - If the distance between b,3 and 7, 3 is 3.5 units,...Ch. 10.1 - Prob. 6ECh. 10.1 - Find the distance between each pair of points: a...Ch. 10.1 - Find the distance between each pair of points: a...Ch. 10.1 - Find the midpoint of the line segment that joins...Ch. 10.1 - Prob. 10E
Ch. 10.1 - Points A and B have symmetry with respect to the...Ch. 10.1 - Points A and B have symmetry with respect to point...Ch. 10.1 - Points A and B have symmetry with respect to point...Ch. 10.1 - Points A and B have symmetry with respect to the...Ch. 10.1 - Prob. 15ECh. 10.1 - Points A and B have symmetry with respect to the...Ch. 10.1 - Points A and B have symmetry with respect to the...Ch. 10.1 - Prob. 18ECh. 10.1 - Points A and B have symmetry with respect to a...Ch. 10.1 - In Exercises 20 to 22, apply the Midpoint Formula....Ch. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - A rectangle ABCD has three of its vertices at...Ch. 10.1 - A rectangle MNPQ has three of its vertices at M0,...Ch. 10.1 - Use the Distance Formula to determine the type of...Ch. 10.1 - Use the method of Example 4 to find the equation...Ch. 10.1 - Use the method of Example 4 to find the equation...Ch. 10.1 - For coplanar points A,B, and C, suppose that you...Ch. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - There are two points on the x-axis that are...Ch. 10.1 - The triangle that has vertices at...Ch. 10.1 - Use the boxing method as suggested in Exercise 33,...Ch. 10.1 - Determine the area of ABC if A=2,1,B=5,3,andC is...Ch. 10.1 - Find the area of ABC In Exercise 35, but assume...Ch. 10.1 - Find the exact volume of the solid that results...Ch. 10.1 - Find the exact volume of the solid that results...Ch. 10.1 - Find the exact volume of the solid that results...Ch. 10.1 - Find the exact volume of the solid that results...Ch. 10.1 - Find the exact lateral area of each solid in...Ch. 10.1 - Find the volume of the solid formed when the...Ch. 10.1 - By definition, an ellipse is the locus of points...Ch. 10.1 - By definition, a hyperbola is the locus of points...Ch. 10.1 - Prob. 45ECh. 10.1 - Use the Distance Formula to show that the equation...Ch. 10.1 - Following a 90 counterclockwise rotation about the...Ch. 10.1 - Consider the point Ca,b. What is the image of C...Ch. 10.1 - Prob. 49ECh. 10.1 - The graphs of the parabolas eith equations y=x2...Ch. 10.1 - Prob. 51ECh. 10.2 - In Exercises 1 to 8, draw the graph of each...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - In Exercises 1 to 8, draw the graph of each...Ch. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Which points lie on the graph of 5x-4y=32? a 4,-3...Ch. 10.2 - Prob. 10ECh. 10.2 - Find the slopes of the lines containing: a 2,-3...Ch. 10.2 - Prob. 12ECh. 10.2 - Find x so that AB- has slope m, where: a A is...Ch. 10.2 - Prob. 14ECh. 10.2 - Are these points collinear? a A-2,5, B0,2, and...Ch. 10.2 - Are these points collinear? a A-1,-2, B3,2, and...Ch. 10.2 - Parallel lines l1 and l2 have slopes m1 and m2,...Ch. 10.2 - Prob. 18ECh. 10.2 - Perpendicular lines l1 and l2 have slopes m1 and...Ch. 10.2 - Prob. 20ECh. 10.2 - In Exercises 21 to 24, state whether the lines are...Ch. 10.2 - In Exercises 21 to 24, state whether the lines are...Ch. 10.2 - In Exercises 21 to 24, state whether the lines are...Ch. 10.2 - In Exercises 21 to 24, state whether the lines are...Ch. 10.2 - Find x such that the points Ax,5, B2,3, and C4,-5...Ch. 10.2 - Find a such that the points A1,3, B4,5, and Ca,a...Ch. 10.2 - Find x such that the line through 2,-3 and 3,2 is...Ch. 10.2 - Find x such that the line through 2,-3 and 3,2 is...Ch. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - In Exercises 29 to 34, draw the line described....Ch. 10.2 - In Exercises 29 to 34, draw the line described....Ch. 10.2 - In Exercises 29 to 34, draw the line described....Ch. 10.2 - Use slopes to decide whether the triangle with...Ch. 10.2 - If A2,2, B7,3, and C4,x are the vertices of a...Ch. 10.2 - If 2,3, 5,-2, and 7,2 are three vertices not...Ch. 10.2 - Three vertices of rectangle ABCD are A-5,1,...Ch. 10.2 - Show that quadrilateral RSTV is an isosceles...Ch. 10.2 - Show that quadrilateral ABCD is a parallelogram.Ch. 10.2 - Quadrilateral EFGH has the vertices E0,0, Fa,0,...Ch. 10.2 - Prob. 42ECh. 10.2 - Prob. 43ECh. 10.2 - Prove that if two lines neither horizontal nor...Ch. 10.2 - Prob. 45ECh. 10.2 - Prob. 46ECh. 10.2 - Pentagon ABCDE has vertices A0,0, B0,b, Cd,c,...Ch. 10.3 - Find an expression for a The distance between a,0...Ch. 10.3 - Find the coordinates of the midpoint of the...Ch. 10.3 - Find the slope of the line containing the points a...Ch. 10.3 - Prob. 4ECh. 10.3 - Prob. 5ECh. 10.3 - Prob. 6ECh. 10.3 - Prob. 7ECh. 10.3 - In Exercises 5 to 10, the real numbers a, b, c,...Ch. 10.3 - Prob. 9ECh. 10.3 - In Exercises 5 to 10, the real numbers a, b, c,...Ch. 10.3 - In Exercises 11 to 16, supply the missing...Ch. 10.3 - In Exercises 11 to 16, supply the missing...Ch. 10.3 - In Exercises 11 to 16, supply the missing...Ch. 10.3 - Prob. 14ECh. 10.3 - In Exercises 11 to 16, supply the missing...Ch. 10.3 - In Exercises 11 to 16, supply the missing...Ch. 10.3 - In Exercises 17 to 22, draw an ideally placed...Ch. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - In Exercises 17 to 22, draw an ideally placed...Ch. 10.3 - In Exercises 17 to 22, draw an ideally placed...Ch. 10.3 - Prob. 22ECh. 10.3 - In Exercises 23 to 28, find the equation...Ch. 10.3 - In Exercises 23 to 28, find the equation...Ch. 10.3 - In Exercises 23 to 28, find the equation...Ch. 10.3 - In Exercises 23 to 28, find the equation...Ch. 10.3 - In Exercises 23 to 28, find the equation...Ch. 10.3 - Prob. 28ECh. 10.3 - The drawing shows isosceles ABC with AC-BC-. a...Ch. 10.3 - The drawing shows parallelogram RSTV. a What type...Ch. 10.3 - Prob. 31ECh. 10.3 - Which formula would you use to establish each of...Ch. 10.3 - Prob. 33ECh. 10.3 - Prob. 34ECh. 10.3 - In Exercises 33 to 36, draw and label a...Ch. 10.3 - In Exercises 33 to 36, draw and label a...Ch. 10.3 - ABCD is a rectangle with vertex A=a,b in Quadrant...Ch. 10.3 - Circle O has its center at the origin and contains...Ch. 10.3 - In RST, SV- bisects RST. Find the coordinates of...Ch. 10.3 - The graph of the parabola y=x2 contains the point...Ch. 10.3 - Prob. 41ECh. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - Prob. 6ECh. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - Prob. 10ECh. 10.4 - Prob. 11ECh. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - Prob. 13ECh. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - In Exercises 1 to 17, complete an analytic proof...Ch. 10.4 - Prob. 18ECh. 10.4 - Use the analytic method to decide what type of...Ch. 10.4 - Use slopes to verify that the graphs of the...Ch. 10.4 - Prob. 21ECh. 10.4 - Use the result in Exercise 20 to find the equation...Ch. 10.4 - Use the result in Exercise 20 to find the equation...Ch. 10.4 - Prob. 24ECh. 10.4 - Prob. 25ECh. 10.4 - Prob. 26ECh. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Based on the result in Exercise 26, describe the...Ch. 10.4 - Based on the result in Exercise 26, describe the...Ch. 10.4 - Suppose that the circle with center 0, 0 and...Ch. 10.4 - Prob. 32ECh. 10.4 - Prob. 33ECh. 10.4 - Complete an analytic proof of the following...Ch. 10.4 - Prob. 35ECh. 10.5 - In Exercises 1 to 4, use division to write an...Ch. 10.5 - Prob. 2ECh. 10.5 - In Exercises 1 to 4, use division to write an...Ch. 10.5 - Prob. 4ECh. 10.5 - Prob. 5ECh. 10.5 - Prob. 6ECh. 10.5 - Prob. 7ECh. 10.5 - Prob. 8ECh. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - Prob. 11ECh. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - Prob. 13ECh. 10.5 - Prob. 14ECh. 10.5 - Prob. 15ECh. 10.5 - Prob. 16ECh. 10.5 - Prob. 17ECh. 10.5 - Prob. 18ECh. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - Prob. 21ECh. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - In Exercises 9 to 24, find an equation of the line...Ch. 10.5 - Prob. 24ECh. 10.5 - Prob. 25ECh. 10.5 - Prob. 26ECh. 10.5 - In Exercises 27 to 32, use graphing to find the...Ch. 10.5 - Prob. 28ECh. 10.5 - Prob. 29ECh. 10.5 - Prob. 30ECh. 10.5 - In Exercises 27 to 32, use graphing to find the...Ch. 10.5 - Prob. 32ECh. 10.5 - In Exercises 33 to 38, use algebra to find the...Ch. 10.5 - Prob. 34ECh. 10.5 - Prob. 35ECh. 10.5 - In Exercises 33 to 38, use algebra to find the...Ch. 10.5 - Prob. 37ECh. 10.5 - Prob. 38ECh. 10.5 - Prob. 39ECh. 10.5 - Prob. 40ECh. 10.5 - Prob. 41ECh. 10.5 - In Exercises 39 to 42, use substitution to solve...Ch. 10.5 - Prob. 43ECh. 10.5 - For isosceles PNQ, the vertices are P-2a,0, N2a,0,...Ch. 10.5 - Prob. 45ECh. 10.5 - Prob. 46ECh. 10.5 - Prob. 47ECh. 10.5 - Prob. 48ECh. 10.5 - Prob. 49ECh. 10.5 - The y-axis along with the graphs of y=-2x+7 and...Ch. 10.6 - In the Cartesian coordinate system below, name the...Ch. 10.6 - Prob. 2ECh. 10.6 - Prob. 3ECh. 10.6 - Find a direction vector for the line containing...Ch. 10.6 - For the line l:x,y,z=2,3,4+n3,-2,5, find a a point...Ch. 10.6 - For the line l:x,y,z=5,3,-2+n1,2,-2, find a a...Ch. 10.6 - Prob. 7ECh. 10.6 - In vector form as in Exercises 5 and 6, find an...Ch. 10.6 - Prob. 9ECh. 10.6 - Prob. 10ECh. 10.6 - In Exercises 11 to 14, find the distance between...Ch. 10.6 - In Exercises 11 to 14, find the distance between...Ch. 10.6 - Prob. 13ECh. 10.6 - Prob. 14ECh. 10.6 - Prob. 15ECh. 10.6 - In Exercises 15 to 18, find the midpoint of the...Ch. 10.6 - Prob. 17ECh. 10.6 - In Exercises 15 to 18, find the midpoint of the...Ch. 10.6 - In Exercises 19 and 20, use the x, y, and...Ch. 10.6 - Prob. 20ECh. 10.6 - Prob. 21ECh. 10.6 - Prob. 22ECh. 10.6 - In Exercises 23 to 26, find an equation for each...Ch. 10.6 - Prob. 24ECh. 10.6 - Prob. 25ECh. 10.6 - Prob. 26ECh. 10.6 - Prob. 27ECh. 10.6 - Prob. 28ECh. 10.6 - Prob. 29ECh. 10.6 - Prob. 30ECh. 10.6 - Prob. 31ECh. 10.6 - Prob. 32ECh. 10.6 - Prob. 33ECh. 10.6 - Prob. 34ECh. 10.6 - Prob. 35ECh. 10.6 - Prob. 36ECh. 10.6 - The line x,y,z=3,4,5+n3,4,-5 intersects the sphere...Ch. 10.6 - Prob. 38ECh. 10.6 - Prob. 39ECh. 10.6 - For the sphers x-12+y+22+z-42=36 and x2+y2+z2=64,...Ch. 10.6 - Does the sphere x2+y2+z2=100 have symmetry with...Ch. 10.6 - Prob. 43ECh. 10.6 - Lines l1: x,y,z=2,0,3+n2,-3,5 and l2:...Ch. 10.6 - The planes with the equation x+2z=12 and y-3z=6...Ch. 10.6 - Prob. 46ECh. 10.6 - Prob. 49ECh. 10.6 - Prob. 50ECh. 10.CR - Find the distance between each pair of points: a...Ch. 10.CR - Prob. 2CRCh. 10.CR - Find the midpoint of the line segment that joins...Ch. 10.CR - Prob. 4CRCh. 10.CR - Find the slope of the line containing each pair of...Ch. 10.CR - Find the slope of the line containing each pair of...Ch. 10.CR - 2,1 is the midpoint of AB-, in which A has...Ch. 10.CR - Prob. 8CRCh. 10.CR - If A has coordinates 2,1 and B has coordinates...Ch. 10.CR - Prob. 10CRCh. 10.CR - Without graphing, determine whether the pair of...Ch. 10.CR - Determine whether the points -6,5, 1,7, and 16,10...Ch. 10.CR - Prob. 13CRCh. 10.CR - Draw the graph of 3x+7y=21, and name the...Ch. 10.CR - Prob. 15CRCh. 10.CR - Prob. 16CRCh. 10.CR - Write an equation for a the line through 2,3 and...Ch. 10.CR - Prob. 18CRCh. 10.CR - Show that the triangle whose vertices are A3,6,...Ch. 10.CR - Prob. 20CRCh. 10.CR - Prob. 21CRCh. 10.CR - Prob. 22CRCh. 10.CR - In Review Exercises 23 and 24, solve the system of...Ch. 10.CR - Prob. 24CRCh. 10.CR - Three of the four vertices of a parallelogram are...Ch. 10.CR - A3,1, B5,9, and C11,3 are the vertices of ABC. a...Ch. 10.CR - Prob. 27CRCh. 10.CR - Prob. 28CRCh. 10.CR - In Review Exercise 27 to 30, supply the missing...Ch. 10.CR - In Review Exercise 27 to 30, supply the missing...Ch. 10.CR - A2a,2b, B2c,2d, and C0,2e are the vertices of ABC....Ch. 10.CR - Prove the statements in Review Exercises 32 to 36...Ch. 10.CR - Prove the statements in Review Exercises 32 to 36...Ch. 10.CR - Prove the statements in Review Exercises 32 to 36...Ch. 10.CR - Prove the statements in Review Exercises 32 to 36...Ch. 10.CR - Prove the statements in Review Exercises 32 to 36...Ch. 10.CR - Determine whether ABC, with vertices A0,0,0,...Ch. 10.CR - Prob. 38CRCh. 10.CR - Prob. 39CRCh. 10.CR - Prob. 40CRCh. 10.CT - In the coordinate system provided, give the...Ch. 10.CT - Prob. 2CTCh. 10.CT - Prob. 3CTCh. 10.CT - Prob. 4CTCh. 10.CT - Complete the following table of x and...Ch. 10.CT - Using the table from Exercise 5, sketch the graph...Ch. 10.CT - Prob. 7CTCh. 10.CT - Prob. 8CTCh. 10.CT - Prob. 9CTCh. 10.CT - Prob. 10CTCh. 10.CT - Prob. 11CTCh. 10.CT - Prob. 12CTCh. 10.CT - Using as few variables as possible, state the...Ch. 10.CT - Prob. 14CTCh. 10.CT - Prob. 15CTCh. 10.CT - Prob. 16CTCh. 10.CT - Prob. 17CTCh. 10.CT - Prob. 18CTCh. 10.CT - Prob. 19CTCh. 10.CT - Prob. 20CTCh. 10.CT - Prob. 21CTCh. 10.CT - Prob. 22CT
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