Question

What is the image of (−10,6) after a dilation by a scale factor of one half centered at the origin?

Answer 1

What is the image of (−8,8) after a dilation by a scale factor of one quarter centered at the origin?

Answer 2

To find the image of the point \((-10, 6)\) after a dilation by a scale factor of \(\frac{1}{2}\) centered at the origin, we can use the formula for dilation:

\[
(x', y') = (kx, ky)
\]

where \((x, y)\) is the original point and \(k\) is the scale factor.

Given the point \((-10, 6)\) and the scale factor \(k = \frac{1}{2}\), we can calculate the new coordinates \((x', y')\) as follows:

\[
x' = k \cdot x = \frac{1}{2} \cdot (-10) = -5
\]

\[
y' = k \cdot y = \frac{1}{2} \cdot 6 = 3
\]

Therefore, the image of the point \((-10, 6)\) after the dilation is

\[
(-5, 3).
\]

Answer 3

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

\[
(x', y') = (kx, ky)
\]

where \((x, y)\) is the original point and \(k\) is the scale factor.

Given the point \((-8, 8)\) and the scale factor \(k = \frac{1}{4}\), we can calculate the new coordinates \((x', y')\) as follows:

\[
x' = k \cdot x = \frac{1}{4} \cdot (-8) = -2
\]

\[
y' = k \cdot y = \frac{1}{4} \cdot 8 = 2
\]

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

\[
(-2, 2).
\]