Question

What is the image of left parenthesis, 0, comma, minus, 3, right parenthesis(0,−3) after a dilation by a scale factor of one third
3
1
​
centered at the origin?
Answer
Attempt 1 out of 2

Answer 1

To find the image of the point \((0, -3)\) after a dilation by a scale factor of \(\frac{1}{3}\) centered at the origin, we apply the dilation transformation using the formula:

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

where \((x, y)\) is the original point, \(k\) is the scale factor, and \((x', y')\) is the image of the point after dilation.

In this case:
- The original point is \((0, -3)\).
- The scale factor \(k\) is \(\frac{1}{3}\).

Now we can apply the formula:

\[
x' = k \cdot 0 = \frac{1}{3} \cdot 0 = 0
\]
\[
y' = k \cdot (-3) = \frac{1}{3} \cdot (-3) = -1
\]

So the image of the point \((0, -3)\) after the dilation is:

\[
(0, -1)
\]