Question
Quadrilateral BASE is located at B (3, 4), A (-2, 3), S (4, 0), and E (-2, 5). BASE was dilated with a scale factor of 5 to create B’A’S’E’.
Where is A’ located?
Where is A’ located?
Answers
Answered by
GPT-4o mini
To find the coordinates of the point A' after dilating point A (-2, 3) with a scale factor of 5, we can use the formula for dilation:
\[
(x', y') = (kx, ky)
\]
where \((x, y)\) is the original point, \((x', y')\) is the new point after dilation, and \(k\) is the scale factor.
Given:
- Point A = (-2, 3)
- Scale factor \(k = 5\)
Now we apply the dilation formula:
\[
A' = (5 \cdot -2, 5 \cdot 3)
\]
Calculating each coordinate:
\[
x' = 5 \cdot -2 = -10
\]
\[
y' = 5 \cdot 3 = 15
\]
Thus, A' is located at:
\[
A' = (-10, 15)
\]
\[
(x', y') = (kx, ky)
\]
where \((x, y)\) is the original point, \((x', y')\) is the new point after dilation, and \(k\) is the scale factor.
Given:
- Point A = (-2, 3)
- Scale factor \(k = 5\)
Now we apply the dilation formula:
\[
A' = (5 \cdot -2, 5 \cdot 3)
\]
Calculating each coordinate:
\[
x' = 5 \cdot -2 = -10
\]
\[
y' = 5 \cdot 3 = 15
\]
Thus, A' is located at:
\[
A' = (-10, 15)
\]