Question

What is the transformation of B(−2, 4) when dilated with a scale factor of ½, using the point (4, 6) as the center of dilation?

A. B'(1, 5)

B. B'(−1, 2)

C. B'(−8, 2)

D. B'(2, 10)

Answer 1

To dilate point B(-2, 4) with a scale factor of 1/2 using the center of dilation at (4, 6), multiply the coordinates of point B by the scale factor, with the center of dilation as the origin.

Step-by-step explanation:

To dilate point B(-2, 4) with a scale factor of 1/2 using the center of dilation at (4, 6), we need to multiply the coordinates of point B by the scale factor, with the center of dilation serving as the origin.

Using the formula for dilation, we can determine the new coordinates of B':

Let B'(x', y') be the new coordinates.

x' = (x - h) * scale factor + h

y' = (y - k) * scale factor + k

Plugging in the values, we get:

x' = (-2 - 4) * 1/2 + 4 = -1

y' = (4 - 6) * 1/2 + 6 = 5

Therefore, the transformation of B(-2, 4) when dilated with a scale factor of 1/2, using the point (4, 6) as the center of dilation, is B'(-1, 5). So, the correct answer is option A.