Question

Here is triangle ABC. Draw the dilation of triangle ABC with center (2,0) and scale factor 2. What are the coordinates of the image of point C when triangle ABC is dilated with center (2,0) and scale factor 2?

A) (4, 0)
B) (3, 0)
C) (2, 0)
D) (1, 0)

Answer 1

To find the image of point C when triangle ABC is dilated with a center of (2,0) and a scale factor of 2, we can multiply the coordinates by the scale factor and add the coordinates of the center.

Step-by-step explanation:

To dilate triangle ABC with a scale factor of 2 and a center of (2,0), we can simply multiply the coordinates of each point by the scale factor and then add the coordinates of the center.

The coordinates of point C are (x,y), so the image of point C will have coordinates (2 + 2(x-2), 0 + 2(y-0)).

Since point C is the center of triangle ABC, its coordinates are (0,0), so the image of point C will have coordinates (2 + 2(0-2), 0 + 2(0-0)).

Simplifying the equation gives us (2 - 4, 0), which is equal to (-2, 0).

Therefore, the correct answer is (A) (-2, 0).