Question

What is the image of left parenthesis, minus, 8, comma, 8, right parenthesis(−8,8) after a dilation by a scale factor of one quarter
4
1
​
centered at the origin?

Answer 1

To find the image of the point \((-8, 8)\) after a dilation centered at the origin with a scale factor of \(\frac{1}{4}\), we can use the 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.

In this case, the original point is \((-8, 8)\) and the scale factor \(k\) is \(\frac{1}{4}\).

Now we will apply the scale factor:

1. For the x-coordinate:
\[
x' = k \cdot x = \frac{1}{4} \cdot (-8) = -2
\]

2. For the y-coordinate:
\[
y' = k \cdot y = \frac{1}{4} \cdot 8 = 2
\]

Thus, the image of the point \((-8, 8)\) after the dilation is:

\[
(-2, 2)
\]