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 and a center point of dilation at the origin.(

1 answer

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

\[ (x', y') = (k \cdot x, k \cdot y) \]

where \( (x, y) \) are the original coordinates of the point, \( (x', y') \) are the coordinates after dilation, and \( k \) is the scale factor.

Given the original points:

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

We will apply the dilation to each of these points with \( k = 3 \).

For Point A(-2, -2):

\[ A' = (3 \cdot -2, 3 \cdot -2) = (-6, -6) \]

For Point B(-4, -3):

\[ B' = (3 \cdot -4, 3 \cdot -3) = (-12, -9) \]

For Point C(-2, -5):

\[ C' = (3 \cdot -2, 3 \cdot -5) = (-6, -15) \]

Summary of Transformed Points:

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

Thus, the coordinates of the points after dilation are:

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