Dilating triangle CDE (C:-2,-2, D:1,-4, E:-3,-4) by 4 centers at origin creates C':(-8,-8), D':(4,-16), E':(-12,-16). Reflecting across y=-x swaps coords, placing C':(-2,2), D':(-4,1), E':(-3,4).
Part (a): Dilation with scale factor 4 centered at the origin
Identify the scale factor and center: We are given a scale factor of 4 and the center of dilation is the origin (0, 0).
Multiply each coordinate by the scale factor:For each vertex of the original triangle CDE, we need to multiply its x and y coordinates by the scale factor of 4.
For C(-2, -2):
C'x = -2 * 4 = -8
C'y = -2 * 4 = -8
Repeat this process for D(1, -4) and E(-3, -4) to find their scaled coordinates D'(4, -16) and E'(-12, -16).
Plot the new triangle: Using the obtained scaled coordinates, plot the triangle C'D'E' on your graph paper or visualization tool. You'll see that C'D'E' is a magnified version of the original triangle, with all its sides and angles stretched by a factor of 4.
Part (b): Reflection in the line y = -x
Identify the reflection line: We are asked to reflect the triangle CDE in the line y = -x. This line passes through the origin and bisects the first and third quadrants.
Swap the coordinates for each vertex: For each point in the original triangle, we need to swap its x and y coordinates.
For C(-2, -2):
C'x = -2 (unchanged as it already lies on the y-axis)
C'y = 2 (swap with x-coordinate)
Repeat this process for D(1, -4) and E(-3, -4) to find their reflected coordinates D'(-4, 1) and E'(-3, 4).
Plot the reflected triangle: Using the obtained reflected coordinates, plot the triangle C'D'E' on your graph paper or visualization tool. You'll see that C'D'E' is a mirror image of the original triangle across the line y = -x. Each vertex will be on the opposite side of the line compared to its original position.