Find the distance between the given point Q and the given line. Q(- 9, 1, 10); x= - 5+ 3t, y = 1-t, z=7+ 4t O A. 6 О В. 5 O C. 5/2 O D. 6/2

Q: Plot the points M(-4,-8), N(3,- 8), and P(1,- 2). Draw MN, NP and MP. (MN means the line segment…

A:

Q: 5. a. Plot these points on the coordinate plane: A = (3,2), B = (7.5, 2), C = (7.5,-2.5), D = (3,…

A:

Q: and PARALLEL to the given line. 2. (-2, 3); y = -x + 4 Y-3ニ-11×+2)

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 28. In the standard (x, y) coordinate plane, the point (2,-6) is the midpoint of the line segment…

A: Given,  In the standard x,y coordinate planeThe point  2,-6  is the midpoint of the line segmentwith…

Q: Find the distance from the point to the line. (-4, – 2,1); x= 5 – t, y = 1- 2t, z = - 6 + 3t

A:

Q: 7. Find the y-intercept for the table below. А. (0,-3) y -26.7 -16 В. (-3, 0) -3 С. (0, 15) 15 24 D.…

A:

Q: r1(t) = (3, –6, 2) +t (-4, 2, –4) r2(t) = (-3, 3, – 10) + t (2, 1, 0) Find the point of…

A: Lines r1 and r2 can be rewritten as follows:

Q: Find the y-intercept of the line 2x+3y-6=0 as a point O a. None O b. (0,2) O c. (2,3) O d. (0,3)

A:

Q: Find an equation of the line L.   L is perpendicular to y=3x through point (2,6)

A: Compare y=3x with y=mx+bSo, m=3Slope=3

Q: e point (-2, 2) and perpendicular to the line 3x+12y =-2.

A:

Q: Match each line with a perpendicular line. A. y = 5x +2 1. the line through (2, 12) and (17, 9) В.…

A:

Q: 10. If M is the midpoint of the line AB where A has coordinates (- 6,5) and B has coordinates (4,3).…

A:

Q: 92° (3b+5)°/ A.O 58.33 В. 29.00 C.O 31.00 D. 32.33

A:

Q: Where a and b are real numbers, (a + b, a – 2b) is the point of intersection for the lines 3x 2x -…

A: We have, point a+b,a-2b is the point of intersection of lines 3x-2y=19 and 2x-5y=9. Therefore, such…

Q: 2. Which line goes down from left to right? O A y = 2x+5 OB.y=2x-6 2c OC y = 2x 2x+ 20

A: The line which goes down from left to right has negative slope.

Q: 3. Which equation models a line that passes through the point (-S, 8) and is parallel to y 3x +2?…

A:

Q: Find the distance dP1, P2 between the given points P1 and P2.   P1=(6,3) P2=(−2,4)

A:

Q: Find the value of Line WY. W 43 – 2x 12x + 1 Y O 43 O 29 O 37 032

A: We know that,  Two tangent line on circle from an external point is of same length.  So, Length of…

Q: B. Find the distance between each pair of points on the coordinate plane. 1. A(12,-2) and B(10,-2)…

A:

Q: Determine the value of a given that y = ax is perpendicular to the line -6x = 3. (Write your answer…

A:

Q: . Rectangle GHU with verlices G(2, -1), H7.-1), K7.-4), and 12.-4): yex

A: We are given the rectangle with G(2, -1), H(7, -1), I(7, -4), and J(2, -4).

Q: Find the distance the point P(0, 2, 8) is to the line through the two points Q(1,-1,4), and R(-1,-4,…

A:

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.