8. Triangle RST has vertices R(10, 0), S(3, 4), and T(4, 2). What is the resulting image of S' after a translation two units down and four units right? Rule:

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: 4. Trapezoid JKLM with vertices J(2, 1) , K(5, 1), L ^ n * (8, - 4) and M(1,-4);90 ° clockwise…

A:

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

A: The objective is to find the value of the given integral where c is the path around the triangle in…

Q: 1. Using Euler's equation, show that the shortest distance between two points (r1, yn, z1) and (r2,…

A: Given, the points are (x1, y1, z1)   and  (x2, y2, z2).

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: 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: 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: Consider AXYZ with vertices X(4, 7), Y(8, 5). and Z(6, 3). Follow the steps to the left to find the…

A:

Q: Graph the image of AUVW after the following glide reflection: Translation (x, y) ► (x - 15, y)…

A: We first find the coordinates of U,V and W U=(3,6), V=(6,3), W=(12,6) Then we apply (x,y)→(x-15,y)…

Q: 6. Find a plane with the P (3, – 4, 5) and contains the line L:= =*

A: It is given that plane passes through (3,-4,5) and the DR's of a given line is 2,-3,5.

Q: 4. Name the coordinates of the image of Q(-2, 5) under a translation along (x, y) → (x + 5, у - 3).

A: We have to find the name the coordinates of the image of Q(-2,5) under a translation along…

Q: Suppose that receiving stations X, Y. and Z are located on a coordinate plane at the points (5,10).…

A:

Q: Use Green's theorem to find $ x? ydr + xdy over a counterclockwise triangular path passing though…

A: To find the line integral ∮x2ydx+xdy by using Green's theorem, First, we need to draw the given…

Q: Show that the distance between the two points z1 and z2 in anArgand diagram is | z1 - z2 | .

A: Argand diagram:  1 It is a plot of complex numbers as point.  2In the complex plane using…

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: 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: 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: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

A:

Q: 2 (6, 0) 10 9- plane is taking off. As it ascends during take-off, it makes a slanted line rainbow…

A:

Q: Show that F(z, y) = (ry, z°y?) is not path independent by considering the line segment from (0,0) to…

A:

Q: 1)calculate xy dady Where D is a triangle with vertices (0,0), (5,0) and (5,5) tip:Don't use the…

A:

Q: 11. Determine whether the lines L₁ given by x=t, y = 1+ 2t, z = 2 + 3t, (with x < t < oo) and L₂…

A:

Q: C is counterclockwise around the rectangle with vertices (0, 0), (5, 0), (5, 3), (0, 3) (a) directly…

A: The given integral is: ∮xy dx+x2 dy C is the counterclockwise around the rectangle with vertices…

Q: Suppose there are three planes in R^3. These three planes could intersect at a single point. What…

A: Any three planes considered at random in space R3 can either intersect or be parallel. There can be…

Q: Suppose ABC- > LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of L?

A: Suppose ABC- &gt; LMN is a reflection across the line x = 0. If A(4, 4) what is the y coordinate of…

Q: Graph the image of AUVW after the following glide reflection: Translation (x, y) (x- 15, y)…

A: Given: The △UVW has done two transformations 1) x,y→x-15,y 2) Reflection across x-axis

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

A:

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

A:

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. How do we obtaln a reflection over the x-axis?

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: Region A is formed by bounding the lines y= T, y = 6, and the y-axis. Determine which pair %3D of…

A: Region A is formed by bounding the lines y=x, y=6 and y-axis. We have to determine which pair of…

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: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: 19. y² dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

A: 19. Given D is the triangular region with vertices (0, 1), (1, 2), (4, 1).We find the given double…

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: Z is a complex variable, z=x+iy Question attached in photo

A: To evaluate the given integral over three different given contours

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: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

A:

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: 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: 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…

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

A:

Q: (5) Let 8. u = 6. --(:)- and y = 1 What is the orthogonal projection of y to the line through u and…

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Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Q: AJKL has vertices J(1,-3), K(4, –3), and L(3,1). Reflect AJKL across the y-axis and then rotate it…

A:

Q: 2. AQRS with vertices Q(2, 5), R(7, 1), and S(-1, 2); translate by (-1, -2)

A: To find the coordinate of translate image we add vector and coordinate of original image.

Q: 10. Triangle JLM with vertices J(-5, 7), L(8, 3), and M(-3, -1): (0, – 5) J'(__ L’(__ M’ (__,

A: