Question

The vertices of a triangle are A(8, -24), B(8,-8), and C (16, -8). If the triangle is dilated by a scale factor of k = 4, what are the coordinates of B'?

O (32,-32)
O (2,-2)
O (64,-32)
O (4,-2)

Answer 1

The coordinates of B' after dilating the triangle by a scale factor of 4 are (32,-32).

Therefore, the correct answer is: option "(32,-32)".

Step-by-step explanation:

To find the coordinates of B' after a dilation by a scale factor of k = 4, we need to multiply the x and y coordinates of B by the scale factor.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

A dilation is a transformation that changes the size of a geometric figure but does not change its shape. The original shape is the pre-image and the dilated shape is the post-image or image.

In this case, since B has coordinates (8,-8), applying the scale factor gives us:

B'(x', y') = (8 * 4, -8 * 4)

= (32, -32)

Therefore, B' will have coordinates (32,-32).

Hence, the correct choice is: (32,-32).