McGraw Hill Glencoe Geometry, 2012
MH
McGraw Hill Glencoe Geometry, 2012 View details
Preparing for Standardized Tests
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Exercise 2 Page 691

We are told that the coordinate grid below shows the final image of a point that was rotated clockwise about the origin, dilated by a scale factor of and shifted units right.

To determine the original coordinates of the point, let's reverse each of these steps starting with the last one. The point was shifted units right, so we need to shift it horizontally units left. Let's do this!

Before that, the point was dilated by a scale factor of Let's recall that if a point is dilated about the origin, both and coordinate of the point are multiplied by the scale factor of the dilation.
In our case the scale of the dilation is so the original coordinates were doubled. From the diagram, we know that the coordinates of the image are Dividing each coordinate by we can find the coordinates of before dilation.
Let's plot it on the coordinate plane!

Before dilation, the point was rotated clockwise around the origin. Hence, to find the initial position of the point, let's rotate it counterclockwise.

We conclude that the original coordinates of the point are