If the vertices of a polygon in counterclockwise order, are ( x1, y1 ) , ( x2, y2 ) , ... , ( xn, yn ) , show that the area of the polygon is A = 1 / 2 [ ( x1y2 - x2y1 ) + ( x2y3 - x3y2 ) + ... + ( xn - 1yn - xnyn - 1 ) + ( xny1 - x1yn ) ] . Use the formula above to find the area of a triangle with vertices (-3, 1), (0, 3), and (3, 2

Q: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

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Q: 17.) What is the vertex of y = - | x | - 2? a. (0, -2) b. (0,2) c. (2, 0) d. (2, -2)

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Q: 2 4x + 9to vertex form by Change the standard form equation y = x" completing the square. -

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Q: b) Use the idea in part (a) to determine an explicit one-to-one correspondence between zt and the…

A: as you asked only the solution for (b) , the solution of the part (b) is given below...

Q: Find the area of the triangle with vertices (0, 0, 0), (-2, -3, -3), and (-2,-2,-5). A =

A: Let,     Then,

Q: the line a1x+b1y+c1=0 and a2x+b2y+c2=0 cut the coordinate axes at concyclic points,then prove that…

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Q: 4. Determine the perimeter and area of the triangle whose vertices are at the origin and the x and…

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Q: evaluate the integral.

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Q: 56. Show that the six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1)…

A: Plotting given six points (1, 0, 0), (−1, 0, 0), (0, 1, 0), (0, −1, 0), (0, 0, 1), and (0, 0, −1).…

Q: 3 Determine what kind of quadrilaterál I formed by the following points: S MI-2,-1), L(1,3), T(5,0)…

A: Given

Q: 18. A) Complete the square for y = 2x² − 12x – 14 B) Determine the coordinates of the vertex. Is it…

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Q: 4. The points P(2,0, 1) and Q(4,2,5) are in R. (a) Find the midpoint between these two points, and…

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Q: Determine the line of intersection between the following planes 12. 5x+2y-7= 9 and -2x+8y +9= = 3.

A: Given: The planes are 5x+2y-7z=9 and -2x+8y+9z=3 To find the line of intersection of the given…

Q: Let C be the upper half (yzo) of the circle x² + y2 = 16 from (4,0) to (-40). √ (ax 2-3y) ds =

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Q: If two vertices of a triangle are (8,4) and (−2,2) and the centroid (intersection of the medians) of…

A: Let (x1,y1) , (x2,y2) and (x3,y3) are three vertices of a triangle the the coordinates of the…

Q: two bees leaving an area in a straight path. Bee's 1 path: r1(t) = + t and Bee's 2 path: r2(s) =…

A: As per the question we are given the trajectory of two Bees and we have to find :whether their…

Q: It is possible for two intersecting lines to be noncoplanar.

A: It is possible for two intersecting lines to be noncoplanar.

Q: The shortest distance from (−7,6,−8) to the xy-plane is

A: Since the plane is a xy-plane so, the point will be (-7,6,0).

Q: D, E, F

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Q: Use an algebraic proof to show that the points A(-3, 1), B(0, 4), C(0, 2), and D(-3, -1) form a…

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Q: If A(1,1,5), B(3,1,7), C(4,1,3) and D(6,1,5) are the nodes of a rhombus (parallelogram). Get the…

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Q: Please

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Q: 1. Given: (x - 5)² = -20(y + 7); what is the vertex? A) (-5, -7) O A OB O O D B) (-5, 7) C) (5, -7)…

A: Find the vertex of the given parabola

Q: 3. Graph. Be sure to label all intercepts. a) y = 2|x + 3|- 4 y-axis x-axis -3 -2 -1 -1 -2 -3 -4 3.…

A: Given: y=2x+3-4 for drawing graph of given expression, first we simplify it so,…

Q: 27. Let ABC be a triangle with vertices A = (-3,0), B = (0, 6), C = (3, 0). Let P be a point on the…

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Q: 10. Which equation represents the parabola that has been vertically stretched by a factor of 5,…

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Q: 10) Use Green's Theorem to eualuate S+10ny +y?)dx + l6xy+ 5a²) dy Toxy+ sa?) dy where C is the…

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Q: A rectangle ha verices at P (6, 6), Q (6, -6), R (-6, -6) and S (-6, 6). The origin is the center of…

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Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

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Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: If the radical axis of the circles x² + y² + 2gx + 2 fy+c= 0 and 2x² + 2y² + 3x +8₂ touches the…

A: Given: Here the radical axis of the circles given x2+y2+2gx+2fy+c=02x2+2y2+3x+8y+2c=0 we have to…

Q: (a) Find the area of the parallelogram with edges v(3,2) and w= = (1, 4).

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