Question

1. given a trapezoid math with coordinates: m(-3, 3), a(-1, 4), t(-1, 1) and h(-3, 1). perform the following transformations in order.

part a - graph and label its image after a dilation with a scale factor of 2. (5 points)
part b - rotate the image from part a, 90° counterclockwise. graph and label its image m\a\t\h\. (5 points)
write the coordinates of each image.
m____ m\____
a____a\____
t____t\____
h____ h\____

Explanation:

Step1: Dilation formula

For a dilation with scale factor \(k = 2\) centered at the origin \((x,y)\to(kx,ky)\).
For point \(M(-3,3)\): \(M'=(-3\times2,3\times 2)=(-6,6)\)
For point \(A(-1,4)\): \(A'=(-1\times2,4\times2)=(-2,8)\)
For point \(T(-1,1)\): \(T'=(-1\times2,1\times2)=(-2,2)\)
For point \(H(-3,1)\): \(H'=(-3\times2,1\times2)=(-6,2)\)

Step2: Rotation formula

For a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\)
For point \(M'(-6,6)\): \(M''=(-6, - 6)\)
For point \(A'(-2,8)\): \(A''=(-8,-2)\)
For point \(T'(-2,2)\): \(T''=(-2,-2)\)
For point \(H'(-6,2)\): \(H''=(-2,-6)\)

Answer:

\(M'(-6,6)\), \(M''(-6,-6)\)
\(A'(-2,8)\), \(A''(-8,-2)\)
\(T'(-2,2)\), \(T''(-2,-2)\)
\(H'(-6,2)\), \(H''(-2,-6)\)