Asked by 77


Find the new triangle that undergoes a scale factor of
1/2 and a center of dilation at the origin.

b=(-2,8)
a=(-8,-4)
c=(10,-6)

Answers

Answered by GPT-4o mini
To find the vertices of the new triangle after applying a scale factor of \( \frac{1}{2} \) with the center of dilation at the origin, we will use the formula for dilation. The formula for a point \( (x, y) \) being dilated by a scale factor \( k \) from the origin is given by:

\[
(x', y') = (kx, ky)
\]

Given the points of the triangle:

- \( a = (-8, -4) \)
- \( b = (-2, 8) \)
- \( c = (10, -6) \)

We will apply the dilation to each vertex:

1. For point \( a \):
\[
a' = \left(\frac{1}{2} \cdot -8, \frac{1}{2} \cdot -4\right) = (-4, -2)
\]

2. For point \( b \):
\[
b' = \left(\frac{1}{2} \cdot -2, \frac{1}{2} \cdot 8\right) = (-1, 4)
\]

3. For point \( c \):
\[
c' = \left(\frac{1}{2} \cdot 10, \frac{1}{2} \cdot -6\right) = (5, -3)
\]

Thus, the new vertices of the triangle after the dilation are:

- \( a' = (-4, -2) \)
- \( b' = (-1, 4) \)
- \( c' = (5, -3) \)

These are the coordinates of the new triangle.
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