Segment MN has endpoints at M (-3, 2) and N (1, 6), If MN is refleeted across the line y=x and then translated three units right and two units down to produce its image M'N', determine the coordinates of the midpoint of M'N', (Use of a separate grid is optional, but

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: 13. Find the distance between the two given parallel planes. x+y-3z = 4 x+y-3z=12

A: Given that:

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

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

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: 6. Quadrilateral STUV with vertices S(-4, 2), T(-2, 6), U(1,7), and V(4, 1) in the x-axis. nioM S'L.…

A:

Q: . Parallelogram JKLM with vertices J(-1, 8), K(5, 6), L(7, -2), and M(1, 0); scale factor: k = 2,…

A:

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

A:

Q: 8) Determine an equation of a line that passes through the point P (5,-2,3) and is parallel to the…

A:

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

Q: Find the shortest distance from the point (1, 5, -5) to the plane 2x + 9y - 3z = 6, using two…

A: Given point is 1,5,-5 and plane is 2x+9y-3z=6

Q: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: Find the distance between the parallel planes.2x + y - 2z = 0 and 2x + y - 2z = 5

A: The given parallel planes are 2x+y-2z=0  and  2x+y-2z=5. The objective is to find the distance…

Q: 3. Line segment JK in the xy-coordinate plane has endpoints with coordinates (-4, 11) and (8, -1).…

A: As per guidelines we can answer only one question at a time, so the first question can be answered…

Q: Consider a circle C in the xy-plane. If it is given that the points (2, 3),(2, −1) and (0, 3) are on…

A: Given points are (2, 3),(2, −1) and (0, 3)

Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

A:

Q: What is the sketch the phrase "three collinear points and a fourth point not on the line of the…

A: Introduction: Dual of any phrase can be find by replacing the conjunction connective with…

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Which graph shows the intersection curve, in the first octant, between a cylinder of equation: (x −…

A: In this question, we need to find the curve which describes the intersection of the surfaces.…

Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: A triangle has vertices A(1,3), B(7,0) and C(4,6). Determine the equation of Euler's line? Hint:…

A: Sketch the triangle:

Q: A Find the Distance from the point (2,-6) to the line 3x+ 4y t6=0 B Find the distance between the…

A:

Q: Find the line of intersection of the planes 2x+y-z=3 and x+2y+z=2. Find the equation of the plane…

A: Solution of part (a) in step2 and step3 and part (b) in step4.

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

A:

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: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

A:

Q: Find the shortest distance between the point A(2, 5, –7) and the plane 3x – 5y + 6z = 9.

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

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

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: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: Line AB 100 mm long is 30 degree and 45degree inclined to HP & VP respectively. End A is 10 mm above…

A: Steps to find HT: Draw xy, one projector and locate VT on it. Draw locus of a110 mm above xy. Take…

Q: 5. Parallelogram RSTU with vertices R(-2, 3), S(2, 4), T(2,-3), U(-2,-4) over the line y = x ty 6.…

A:

Q: A line h passes through a point P(2,–4,3) and is parallel to the line of intersection between planes…

A: We will use cross product to find vector parallel to h and then check it will be parallel or…

Q: Find the minimum distance from the point (8, 3, 4) to the plane x - y + z = 4. (Hint: To simplify…

A:

Q: 5. Quadrilateral WXYZ with vertices W(0, -4), X(13, 0), Y(9, -12), and 2(5, -12); scale factor: k -…

A:

Q: Findauihtvectorhermat to thesuFace X Y +X2=1 et the Point (-1,1,1)

A:

Q: B) The line passes through the point (2,4,5) and perpendicular to the plane 2x+y- intersects the x-y…

A: Given that the line passes through the point (2, 4, 5) and perpendicular to the plane 2x+y-5z =21

Q: 3. Find the shortest distance from the origin to the plane x – 2y – 2z = 3. |-

A: Here I am attaching image so that you understand each and every step.

Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Find the shortest distance from the point (2,0,–3) to the plane x + y + z = 1. . Use Lagrange…

A:

Q: Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer…

A: Given point 1,3,-1 and the plane 3x-4y+5z=6

Q: Find the distance of the point (3,8,2) from the line x-1 -y+3 -z+2 measured -3 2 -4 parallel to the…

A: Given point 3, 8, 2Given line - x-12=-y+3-4=-z+2-3Let the parameters be equal to an arbitrary…

Q: -) Find the distance from the point (4, 22, 6) down to the ry-plane. ) Find the distance from the…

A:

Q: Q = (-1,3,–1) on the plane Find the point P nearest to x – 4z = 2

A: Given, Q=(-1,3,-1) x-4z=2 (equation of plane) x-4z-2=0

Q: Among all the points on the graph of z = 10 - x2 - y2 that lie above the plane x + 2y + 3z = 0, find…

A:

Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

A: