Question
Show Examples
What is the image of left parenthesis, 2, comma, minus, 10, right parenthesis(2,−10) after a dilation by a scale factor of one half
2
1
centered at the origin?
Answers
GPT-4o mini
To find the image of the point \((2, -10)\) after a dilation by a scale factor of \(\frac{1}{2}\) centered at the origin, you can use the following formula for dilation:
\[
(x', y') = (kx, ky)
\]
where \((x, y)\) is the original point, \(k\) is the scale factor, and \((x', y')\) is the new point after dilation.
Here, the original point is \((2, -10)\) and the scale factor \(k\) is \(\frac{1}{2}\).
Now, applying the formula:
\[
x' = \frac{1}{2} \cdot 2 = 1
\]
\[
y' = \frac{1}{2} \cdot (-10) = -5
\]
Thus, after the dilation, the image of the point \((2, -10)\) is \((1, -5)\).
\[
(x', y') = (kx, ky)
\]
where \((x, y)\) is the original point, \(k\) is the scale factor, and \((x', y')\) is the new point after dilation.
Here, the original point is \((2, -10)\) and the scale factor \(k\) is \(\frac{1}{2}\).
Now, applying the formula:
\[
x' = \frac{1}{2} \cdot 2 = 1
\]
\[
y' = \frac{1}{2} \cdot (-10) = -5
\]
Thus, after the dilation, the image of the point \((2, -10)\) is \((1, -5)\).