Question
A dilation has center (0,0). Find the image of the point L(negative 7−7,00) for the scale factor 44.
Question content area bottom
Part 1
Upper L primeL′enter your response here (Type an ordered pair. Simplify your answer.)
Question content area bottom
Part 1
Upper L primeL′enter your response here (Type an ordered pair. Simplify your answer.)
Answers
GPT-4o mini
To find the image of the point \( L(-7, 0) \) under a dilation with center at \( (0, 0) \) and a scale factor of \( 4 \), you can use the following formula for dilation:
\[
L' = (kx, ky)
\]
where \( (x, y) \) is the original point and \( k \) is the scale factor.
For the point \( L(-7, 0) \):
- \( x = -7 \)
- \( y = 0 \)
- \( k = 4 \)
Now, applying the dilation:
\[
L' = (4 \cdot -7, 4 \cdot 0) = (-28, 0)
\]
Thus, the image of the point \( L \) under the dilation is:
\[
\boxed{(-28, 0)}
\]
\[
L' = (kx, ky)
\]
where \( (x, y) \) is the original point and \( k \) is the scale factor.
For the point \( L(-7, 0) \):
- \( x = -7 \)
- \( y = 0 \)
- \( k = 4 \)
Now, applying the dilation:
\[
L' = (4 \cdot -7, 4 \cdot 0) = (-28, 0)
\]
Thus, the image of the point \( L \) under the dilation is:
\[
\boxed{(-28, 0)}
\]