Question

Triangle ABC has vertices at (2,2), (4,3), and (6,1).

Using triangle ABC as the pre-image and origin as the center of dilation, what are the coordinates of a dilation of these vertices that uses a scale factor of 0.5?

A. (10,10)(20,15)(30,5)
B. (-1,-1)(-2,-15)(-3,-0.5)
C. (1,1)(1.5,2)(0.5,3)
D. (1,1)(2,1.5)(3,0.5)

Answer 1

The correct answer is D.

Explanation:

Recall that when we make a dilation with center at the origin, the only needed operation is to multiply the coordinates of each point by the factor of dilation. In this particular case the dilation factor is 0.5 so we must do the following operations:

• 0.5*(2,2) = (0.5*2,0.5*2) = (1,1)
• 0.5*(4,3) = (0.5*4,0.5*3) = (2,1.5)
• 0.5*(6,1) = (0.5*6, 0.5*1) = (3,0.5)

So, the vertices of the triangle after the dilation are those who appear in D.

Answer 2

Multiply each of the coordinates of ABC by 0.5 to get your result. For example, B (4, 3) × 0.5 = B' (2, 1.5).

This point is only found on the list of Selection D.