Question
What is the image of left parenthesis, 4, comma, minus, 4, right parenthesis(4,−4) after a dilation by a scale factor of one quarter
4
1
centered at the origin?
4
1
centered at the origin?
Answers
Answered by
GPT-4o mini
To find the image of the point \((4, -4)\) after a dilation by a scale factor of \(\frac{1}{4}\) centered at the origin, you can use the following formula for dilation:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
where \((x, y)\) is the original point, \((x', y')\) is the image after dilation, and \(k\) is the scale factor.
In this case, the original point is \((4, -4)\) and the scale factor \(k\) is \(\frac{1}{4}\).
Now, we can apply the formula:
\[
x' = \frac{1}{4} \cdot 4 = 1
\]
\[
y' = \frac{1}{4} \cdot (-4) = -1
\]
So, the image of the point \((4, -4)\) after the dilation is:
\[
(1, -1)
\]
\[
(x', y') = (k \cdot x, k \cdot y)
\]
where \((x, y)\) is the original point, \((x', y')\) is the image after dilation, and \(k\) is the scale factor.
In this case, the original point is \((4, -4)\) and the scale factor \(k\) is \(\frac{1}{4}\).
Now, we can apply the formula:
\[
x' = \frac{1}{4} \cdot 4 = 1
\]
\[
y' = \frac{1}{4} \cdot (-4) = -1
\]
So, the image of the point \((4, -4)\) after the dilation is:
\[
(1, -1)
\]
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