# Rotation of a Quadrilateral

When rotating 90° about the origin counterclockwise, the point will be as far above or below the origin as it was previously right or left. In other words, the coordinate (x,y) when rotated counterclockwise about the origin becomes (-y,x).

## Rotation of a Quadrilateral

Points A, B, C, and D have coordinates (2, 3), (-1, 5), (- 2, -2), and (4, -3) respectively. If quadrilateral ABCD is rotated 90 degrees counterclockwise about the origin to create quadrilateral A’B’C’D’, what are the coordinates of A’, B’, C’, and D’?

When rotating 90 degrees about the origin counterclockwise, the point is now as far above or below the origin as it was previously right or left respectively. Now it’s as far left or right of the origin as it was above or below the origin.

In other words, if you’ve got a coordinate (x, y), then when it’s rotated counterclockwise about the origin, it’s old x coordinate is the new y coordinate and its old y coordinate is the negative of its new x coordinate. To find the coordinates of A’, B’, C’, and D’, we’re going to apply these changes to the coordinates starting with A.

A was (2, 3), so the new coordinates for A are- we take our y and our new x is the negative of that y, so -3. Our new y is the x coordinate from the original point, so 2. Now for B. B was originally (-1, 5), so the new coordinates for point B- the old y coordinate, the negative of that old y coordinate is now our x, so -5 is now x.

Our old x coordinate is now our y coordinates, so -1 is y. Now for C. C was (-2, -2). To rotate it 90 degrees counterclockwise about the origin, our new x coordinate is the negative of our y coordinate. The negative of -2 is positive 2, and our new y coordinate is our x coordinate, which is -2.

Then, finally, D was (4, -3), so the new coordinate for D- our x coordinate is the negative of our y coordinate, so the negative of -3 would be 3. Our y coordinate is our old x coordinate, so positive 4. There are the new coordinates for our quadrilateral that was rotated 90 degrees about the origin. You could use these coordinates to then graph the new rotated quadrilateral.

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by Mometrix Test Preparation | Last Updated: August 15, 2019