9. Square ABCD with vertices A(-7, 5), B(-4, 7), C(-2, 4), and D(-5, 2): 90° counterclockwise 10. Rectangle WXYZ with vertices W(-3, -5), X(1, -1), Y(3, -3), and Z(-1, -7): 180° A': C': Y': B: D': X': Z':

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: show.. that the line in.which. the planes.X+zy-223D5 and. 5X-zy.-7=D0.jntersect.is. pavalle.to. the…

A:

Q: Draw rhombus WXYZ with diagonals WY and XZ. Let WY name the longer diagonal. a) How are diagonals WY…

A:

Q: 3. Rectangle PORS with vertices P(5, 15). Q(15, 15). R(15, 10), and S(5, 10): A- 4/5 4. Rhombus WXYZ…

A: Plot the given points and its scaled version

Q: Evaluate the line integral along the given path(s).

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

Q: Q1/ Find the angle between the planes 3 x -6y - 2z = 15 and 2 x +y– 2z = 5

A: Explanation of the answer is as follows

Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

A:

Q: If quadrilateral ABCD was rotated 270 degrees counterclockwise about point D, what would be the…

A: Use coni method to find the rotation of point B after 270 degree rotation, zB'-zDzB-zD=cosθ+isinθ…

Q: Find the intersection of the plane 4x – 6y – 7z = 10 and the line r(t) = (- 8, – 3, 3)t + (4, 1, 5).…

A:

Q: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: b. Find the distance from the point (2, –2, 3) to the intersection of the planes 2x – y + 3z = 1 and…

A:

Q: Find the acute angle (in degrees) between the planes Sz + 3y +5z 1 and 2z

A: P1 denotes plane 1 P2 denotes plane 2

Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

A:

Q: Find the coordinates of the reflection without using the coordinate plane. Q(-3,5) over the y-axis.

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the point P on AB that is one-third of the distance from A(-1, 2) to B(8, 5). y 10 8. P -10-8…

A: Given points A(-1, 2) and B(8, 5). To find point P which divides the line segment in the ratio 1:3.…

Q: Sketch parallelogram-INDY with diagonals intersecting at point P in the box below on the left. If IP…

A: Given,           A parallelogram INDY with diagonals intersevting at point P.           IP=3x,…

Q: 2. Trapezoid QRST with vertices Q(3, 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

A: Rules for counterclockwise rotation about the origin: 90°  : x,y →-y,x180°: x,y →-x,-y270°: x,y…

Q: Determine the angle between the planes: x-z+7=0 2x +y-z+8 = 0

A: Solution :--

Q: Calculate , (7xy+ 3e²) dS, where S is the triangle with vertices (0,0, 3), (1,0, 2), and (0, 4, 1).…

A: Given vertices of triangle are 0,0,3 ,1,0,2 ,0,4,1 Let the equation of plane through these points…

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

A:

Q: Find the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: Find the point on the plane 2x + y + 4z = 5 that is closest to the point P(4, 3, 5). (x, y, z) =…

A: We are given a plane 2x + y +4z = 5, and we are asked to find the co-ordinates of the point on the…

Q: 2. Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2).

A:

Q: Find the condition for the points (a,0) ,(h,k),(0,b) when ab is not equal to 0 to be collinear

A:

Q: If the image of the point (1 -2 3) in the plane 2x+3y-z=7 is the point x, y, z then the value of…

A: Let's first understand the

Q: 7. Reflect parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,–4) in the line y = -x.…

A: Reflection in Y axis  : (x , y ) → (-x , - y )

Q: 12 Which point is equidistant from the planes T1:- 2x +y- 2z + 3 = 0 and 73: - 2x + y- 2z + 21 = 0?…

A: Option B is correct :- (explained below)

Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: 2. Trapezoid QRST with vertices Q(3. 1), R(5, 2), S(10, 0), and T(4, -3); 270° counterclockwise…

A:

Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: Find the condition for the points (a, 0), (h, k), (0, b)when ais not equals to U to be collinear

A: We have to find the condition

Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: Find the value of k for which the planes: 2x-ky+4z=1 and kx+y-3z%3D2 are orthogonal.

A: we have to find the value of k for which the planes 2x-ky+4z=1 and kx+y-3z=2 are orthogonal.

Q: Find the relationship between x and y such that the point (x,y) is equidistance from the points…

A:

Q: Find the distance between the given parallel planes. 2x - 3y + z = 8, 4x - 6y + 2z = 1

A: The solution are next step

Q: Find the coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

A:

Q: The cosine of the angle between the planes 2x - y +2z - 3 = 0 and 3x + 2y – 6z – 11 = 0 is (a)를 (b)를…

A: We'll answer the first question since the exact one wasn't specified. 13. For two planes given by…

Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: Find the angle between the planes x+2y+2z-5=0 and 3x+3y+2z-8=0

A:

Q: 8. Find the angles between the planes r + y = 1, 2x + y – 2z = 2

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: 5. Rhombus CDEF with vertices C(-5, 5). D(-1, 7), E(-3, 3). and F(-7, 1): 270° counterclockwise C:…

A: Since you have posted multiple questions so according to our guidelines we will solve only first…

Q: Find the value of o(4x + y)dy - rydy where C is the path around the triangle in the counterclockwise…

A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

Q: +4z=8 and

A: The equation of the plane as, x+z=1orx+0y+z=1 Here, a1 =1,b1 =0,c1 =1. and x+2y+4z=8 Here, a2 =1,b2…

Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

A:

Q: What are coordinates of AABC with A(-4,3), B(3,1), and C(2,-5) after a reflection over the line y=x?

A: The coordinates of triangle ∆ABC are A-4, 3, B3, 1 and C2, -5To find the reflection over the line…

Q: If point A is reflected over the y-axis and its original location was (2,3), where is its new…

A:

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: , in general form (x + y2 + Bx + Cy + D = 0), centered a he lines 2x + y + 10 = 0 and x - 2y - 5 = 0…

A: We have to find the equation of a circle whose center is the point of intersection of,  2x+y+10=0…

Q: Find the z-coordinate of the foot of the perpendicular from A(1, 1, 1) on the line joining B(1, 4,…

A: We will solve the problem.

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

A: