Rectangle WXYZ with vertices H(- 3, - 4), X(0, - 5); Y(- 2, - 11) and Z(-5,-10);1; 180 degrees rotation about N(2, - 3)

Q: 2. (a) Show that the points (-2x, 5x), (0, 4x), (6x, x) are collinear.

A: Given that: (-2x, 5x), (0, 4x) , (6x, x)

Q: 5. Square JKLM with vertices J(-3, 5), K(0, 8). L(3, 5), and M(0, 2); 90° clockwise about P(-4, 0)…

A: If the point (-y,x) rotate 90 degrees clockwise about the point (a,b), then the coordinates of the…

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: (1) Find an equation for the plane that passes through the point (–1,2,2) and contains the line of…

A: Given: Equation of planes x+y-z=5⇒x+y-z-5=0 and 3x-y+5z=3⇒3x-y+5z-3=0 and point -1,2,2, To find: The…

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and 0(2,-3,4).

A:

Q: What are the new coordinates of point M (-8, 3) after a reflection in the line y =x? O (3,-8) O(8,…

A:

Q: Trapezoid PGRS with vertices P(-6, 2), G(-2 -0, R(-2 -3), and S(-6, -6), reflect in the linex-1 (4)…

A: We need to draw transformed image.

Q: A quadrilateral ABCD with coordinates A(-5, 3), B(-5, 1), C(-4, 1), and D(-2, 5), is reflected…

A: We have to find the co ordinate of B".

Q: 8. Find the equation of the plane that contains the points P,(3,1,–2), P2(0, –2, 1), and P3(-2, –5,…

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

Q: Graph the image of trapezoid BCDE after a rotation 270° counterclockwise around the origin. 10 4. 2.…

A: topic - rotation about origin

Q: Find the coordinates of the centroid of the triangles whose vertices are: a. (5.7), (1, -3), (-5.1);…

A:

Q: 20) Find the equation for the plane in 3-space passing through the points (2,3,2), (0, -4, 3) and…

A:

Q: The plane through the points (8,4,5), (-3,7,-5), (7,8,-3) has equation Ax + By+ Cz = If A = 16 find…

A:

Q: Find the equation of a plane passing through (2,1,3), (3, –1,5), and (1,2, –3).

A: Equation of plane

Q: 7. Find the centroid of a triangle whose vertices are (2, 3), (-4, 6) and (2, -6). В. (0, -1) A. (0,…

A:

Q: Identify the new coordinates of (-4, 1) after a reflection across the y-axis. y 10- 8- 6- 4+ ((6, 1)…

A: Given  Coordinate (-4,1)

Q: L' M' Which describes how the transformation affects the coordinates of the vertices of trapezoid…

A:

Q: 2. Find an equation of the sphere that passes through the point (2, 3, –1) and has center (-3, –1, –…

A:

Q: Graph the image of rectangle CDEF after a rotation 180° counterclockwise around the origin. 10 4 2…

A: If we rotate 180 degree about origin the sign of the coordinates will reversed

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: 4- Find an equation of the plane that passes through the given points (-2, 1, 1), (0, 2, 3), and (1,…

A:

Q: 2. Find the equation of the plane through the points (1, -3,2), (3,0,– 1), and (0,5,5).

A:

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

A:

Q: Find the coordinates of the vertices of the polygon after the given translation to a new position in…

A:

Q: 10수 2 T -10 -8- -4 -2 2. 8. 10 -2 -4 -6 4. 6. 4- to

A:

Q: Find an equation of the plane that passes through the points M(1,2,3), N(-3,-2,5), and O(2,-3,4).

A:

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

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

A:

Q: The equation of the plane that contains the three points (0, 4, 4), (4, 0, 4), and (4, 4, 1) is

A:

Q: When X and Y are moving in the same direction the cross-products are likely to be

A: Cross Product :  It is a vector operation that acts on vectors in three dimensions and results in…

Q: 6) Find the distance between the point (1, -4, -3) and the plane 2x – 3y + 6z = - 1.

A:

Q: Find the image of the unit cube with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), (0, 1, 0), (0, 0, 1),…

A:

Q: 9. Find an equation for the plane containing the points (3,1, 4), (–1, –1,-1), and (0,2,2).

A:

Q: 4. (5) Find the equation of the plane passing through the points. Simplify the equan (2,0,1),…

A:

Q: 2. Find the equation of the plane through the points (1,–3,2), (3,0,–1), and (0,5,5).

A: The solution is given as follows

Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: Find the equation of plane with vertices P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

A: We have to find

Q: Find the symmetric equations of the L that is parallel to the two planes x + 2y - z= 2 and x + 6y+ z…

A: Given: Two planes, P1: x+2y-z=2, P2: x+6y+z=-3, Point P1, 2, 3

Q: 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

A: Given problem:- 4. Find an equation for the plane through (1, 3, 4), (2, 2, 3), and (3, 2, 1).

Q: Find the equation of a plane passes through (1, 2, 3), (3,2,1) and (-1, -2, 2) ○ 4x - 3y + 4z = 10…

A: This question is based on finding equation of plane that passes through 3 points.

Q: Find // (4x + 5y)dA where R is the R parallelogram with vertices (0,0), (-3,1), (2,4), and (-1,5).…

A:

Q: Find the equation of the plane containing the x-axis and passing through the point (4,3,1/5)

A:

Q: 1 What is the image of the point (-4, -2) after the reflection over the line y = - x- 1?

A: follow next step

Q: Graph the image of rectangle TUVW after a rotation 180° counterclockwise around the origin. 101" V T…

A: Topic = Geometry

Q: What will be the new coordinates of point M (-5, -7) after a rotation of 270° counterclockwise about…

A: To fins the new coordinate of point M (-5,-7) after a rotation of 270° anticlockwise about the…

Q: Which of the following point is the projection of the point (0, 4, 2) on the yz-plane?

A: In this question we have to find the projection of the point on the yz-plane.

Q: Suppose a surface in three-dimensional space has the equation ax^2+bx+cy^2+dy=z  and it contains the…

A: A given set of points can be assumed to be on a surface given by an equation when the each of…

Q: 3. 4. Circumscribing the triangle with vertices (a, U), (a, d), (U, %). 2a = 0. Ans. z2 + y+ ax- ay…

A: In the question we have to find equation of circle circumscribed in a triangle. NOTE - As per…