Question
What is the image of left parenthesis, minus, 12, comma, 8, right parenthesis(−12,8) 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 \((-12, 8)\) after a dilation centered at the origin with a scale factor of \(\frac{1}{4}\), you can use the formula for dilation:
\[
(x', y') = (kx, ky)
\]
where \((x, y)\) is the original point, \((x', y')\) is the dilated point, and \(k\) is the scale factor.
In this case, the original point is \((-12, 8)\) and the scale factor \(k\) is \(\frac{1}{4}\).
Now, we can calculate the dilated coordinates:
\[
x' = k \cdot x = \frac{1}{4} \cdot (-12) = -3
\]
\[
y' = k \cdot y = \frac{1}{4} \cdot 8 = 2
\]
Therefore, the image of the point \((-12, 8)\) after the dilation by a scale factor of \(\frac{1}{4}\) centered at the origin is \((-3, 2)\).
\[
(x', y') = (kx, ky)
\]
where \((x, y)\) is the original point, \((x', y')\) is the dilated point, and \(k\) is the scale factor.
In this case, the original point is \((-12, 8)\) and the scale factor \(k\) is \(\frac{1}{4}\).
Now, we can calculate the dilated coordinates:
\[
x' = k \cdot x = \frac{1}{4} \cdot (-12) = -3
\]
\[
y' = k \cdot y = \frac{1}{4} \cdot 8 = 2
\]
Therefore, the image of the point \((-12, 8)\) after the dilation by a scale factor of \(\frac{1}{4}\) centered at the origin is \((-3, 2)\).
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