A dilation has center​ (0,0). Find the image of the point ​L(negative 7−7​,00​) for the scale factor 44.

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Part 1
Upper L primeL′enter your response here ​(Type an ordered pair. Simplify your​ answer.)

1 answer

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:

\[ \boxed{(-28, 0)} \]