Question

Suppose that triangle ABC is dilated to A'B'C' by a scale factor of 4 with a center of dilation at the origin. What is the distance from the center of dilation to the midpoint of B'C'?

Answer 1

The distance from the center of dilation to the midpoint of B'C' is 4 times the original distance from the center to the midpoint of BC, given the dilation scale factor is 4.

Step-by-step explanation:

To find the distance from the center of dilation to the midpoint of B'C', we use the properties of dilations in geometry. Since triangle ABC is dilated with a scale factor of 4, every length in triangle ABC is multiplied by 4 to get the corresponding length in triangle A'B'C'. If the original distance from the center of dilation (the origin) to the midpoint of BC was 'x', then after the dilation, the distance from the center (the origin) to the midpoint of B'C' is 4x. If the original distance x is known, we calculate the dilated distance by multiplying x by the scale factor of 4.