Question

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.(2 points)

A′= (__,__) B′= (__,__) C′= (__,__)

Answer 1

To find the coordinates of the points after a dilation with a scale factor of 3 from the origin, we can use the formula for dilation. Given a point \((x, y)\) and a scale factor \(k\), the new coordinates \((x', y')\) after dilation are given by:

\[
x' = k \cdot x
\]
\[
y' = k \cdot y
\]

In this case, the scale factor \(k = 3\).

Now applying this to each vertex:

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

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

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

After calculating all points, we find:

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

Thus, the final coordinates after dilation are:

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