Question

Triangle DJM has vertices D(-1, 2), J(-3, 4), . What are the coordinates of the image of triangle DJM after a dilation by a scale factor of 2 and then a rotation 90° counterclockwise?

A) (-4, 0), (-6, 2), (-2, 4)
B) (-2, 4), (-4, 6), (0, 2)
C) (0, -4), (2, -6), (4, -2)

Answer 1

The image of triangle DJM after a dilation by a scale factor of 2 and then a rotation 90° counterclockwise has coordinates (-4, 0), (-8, -6), and (0, -2).

Step-by-step explanation:

To find the image of triangle DJM after a dilation by a scale factor of 2 and then a rotation 90° counterclockwise, we first apply the dilation by multiplying the x and y coordinates of each vertex by the scale factor of 2. After the dilation, the coordinates of triangle DJM become D'(-2, 4), J'(-6, 8), and M'(-2, 0). Now, for the rotation 90° counterclockwise, we swap the x and y coordinates of each vertex and negate the new x coordinates. After the rotation, the coordinates of triangle DJM become D''(-4, 0), J''(-8, -6), and M''(0, -2). Therefore, the coordinates of the image of triangle DJM after the dilation and rotation are (-4, 0), (-8, -6), and (0, -2), which corresponds to option C).