Question

If triangle ABC has vertices A(1, 2), B(-1, -1), and C(0, -2), which of the following coordinates is B’ of the dilation using the scale factor 4?

Answer 1

B' = (-4, -4)

Explanation:

Dilation: A type of transformation that makes the pre-image larger or smaller without changing its shape.

Center of a dilation: a fixed point about which all points are dilated.

Given:

• A = (1, 2)
• B = (-1, -1)
• C = (0, -2)
• Scale factor = 4

For dilation when the center of dilation is the origin (0, 0), simply multiply the coordinates of the vertices of the pre-image by the given scale factor to find the image under dilation:

Therefore:

A' = (1 x 4, 2 x 4) = (4, 8)

B' = (-1 x 4, -1 x 4) = (-4, -4)

C' = (0 x 4, -2 x 4) = (0, -8)

Answer 2

Answer: B'(-4, -4)

Given : A(1, 2), B(-1, -1), C(0, -2)

"Focusing on B coordinates"

If the points are dilated with a scale factor of 4

Then new coordinates : (-1, -1) × 4 = B'(-4, -4)