Question

A dilation has center​ (0,0). Find the image of the point ​A(negative 5−5​,55​) for the scale factor 1.21.2.
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Part 1
Upper A primeA′enter your response here
​(Simplify your answer. Type an ordered​ pair.)

Answer 1

To find the image of the point \( A(-5, 5) \) under a dilation with center \( (0, 0) \) and a scale factor of \( 1.2 \), you can use the formula:

\[
A' = (kx, ky)
\]

where \( k \) is the scale factor and \( (x, y) \) are the coordinates of point \( A \).

In this case:
- \( k = 1.2 \)
- \( A(-5, 5) \), so \( x = -5 \) and \( y = 5 \).

Calculating the new coordinates:

\[
A' = (1.2 \cdot -5, 1.2 \cdot 5)
\]

Calculating each coordinate:

1. \( 1.2 \cdot -5 = -6 \)
2. \( 1.2 \cdot 5 = 6 \)

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

\[
A' = (-6, 6)
\]

So, in ordered pair form, the answer is:

\[
\boxed{(-6, 6)}
\]