Triangle ABC

Question

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
and a center point of dilation at the origin

Answer 1

To perform a dilation from the origin with a scale factor of \( k \), you multiply each coordinate of the point by the scale factor \( k \).

Given the points:

• \( A(-2, -2) \)
• \( B(-4, -3) \)
• \( C(-2, -5) \)

Let's perform the dilation with scale factor \( k = 3 \):

1. For point \( A \): \[ A' = (k \cdot x_A, k \cdot y_A) = (3 \cdot -2, 3 \cdot -2) = (-6, -6) \]

2. For point \( B \): \[ B' = (k \cdot x_B, k \cdot y_B) = (3 \cdot -4, 3 \cdot -3) = (-12, -9) \]

3. For point \( C \): \[ C' = (k \cdot x_C, k \cdot y_C) = (3 \cdot -2, 3 \cdot -5) = (-6, -15) \]

Thus, the coordinates after dilation are:

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