Question

Graph the image of the figure after a dilation with a scale factor of 3 centered at (2, −7).

Use the Polygon tool to graph the quadrilateral by connecting all its vertices.

Answer 1

Explanation:

Each point moves 3 times the distance from the center of dilation that it was.

You can compute the new coordinates by ...

L = P - O . . . . . the length from O to P is P-O for some point P and origin O

Then 3 times that distance is

3L = 3P -3O

We want to find the point P' that is 3L from O, so we add this distance to the coordinates of O. We get ...

P' = 3L +O = 3P -3O +O

P' = 3P -2O

So, for the lower left point A(-2, -7), the dilated image point A' is ...

A' = 3(-2, -7) -2(2, -7) = (-6, -21) +(-4, 14) = (-10, -7)

That is, ...

A' = 3A +(-4, 14)

The coordinates of the remaining points can be found similarly.

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On a graph, it is usually fairly easy to count the grid squares in each direction between the point of interest and the center of dilation. The image point is 3 times the distance in each direction (horizontally, vertically).