Question

What is the image of left parenthesis, minus, 2, comma, minus, 9, right parenthesis(−2,−9) after a dilation by a scale factor of 33 centered at the origin?

Answer 1

To find the image of the point \((-2, -9)\) after a dilation by a scale factor of 33 centered at the origin, we use the following formula for dilation centered at the origin:

\[
(x', y') = (k \cdot x, k \cdot y)
\]

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

In this case:
- The original point \( (x, y) = (-2, -9) \)
- The scale factor \( k = 33 \)

Now we apply the formula:

1. Calculate the new x-coordinate:
\[
x' = 33 \cdot (-2) = -66
\]

2. Calculate the new y-coordinate:
\[
y' = 33 \cdot (-9) = -297
\]

Therefore, the image of the point \((-2, -9)\) after the dilation is:

\[
\boxed{(-66, -297)}
\]