Triangle ABC has vertices point A(−2,−2), point B(−4,−3), and point C(−2,−5). Find the coordinates of A′, B′, and C′ after a dilation with a scale factor of 3

Question

and a center point of dilation at the origin.(2 points)
A′= (
)
B′= (
)
C′= (
)

Answer 1

To find the coordinates of A', B', and C' after a dilation with a scale factor of 3 and a center point of dilation at the origin, we can use the formula for dilation:

(x', y') = (k * x, k * y)

Where (x, y) are the original coordinates, (x', y') are the coordinates after dilation, and k is the scale factor.

For point A(-2, -2):

A' = (3 * -2, 3 * -2) = (-6, -6)

So, A' is (-6, -6).

For point B(-4, -3):

B' = (3 * -4, 3 * -3) = (-12, -9)

So, B' is (-12, -9).

For point C(-2, -5):

C' = (3 * -2, 3 * -5) = (-6, -15)

So, C' is (-6, -15).

Therefore:

A' = (-6, -6)
B' = (-12, -9)
C' = (-6, -15)