# Video: Finding the Coordinates of the Vertices of a Quadrilateral after Reflection

What is the image of π΄π΅πΆπ· under the rotation (π₯, π¦) β (βπ¦, π₯)?

03:30

### Video Transcript

What is the image of π΄π΅πΆπ· under the rotation π₯, π¦ maps to negative π¦, π₯?

Now weβve been given a figure over here which shows shape π΄π΅πΆπ·. Now the coordinates of point π΄ are four, three.

So the π₯-coordinate is four and the π¦-coordinate is three. The coordinates of point π΅ are five comma three. So the π₯-coordinate is five and the π¦-coordinate is three. Point πΆ is at five, four with an π₯-coordinate of five and a π¦-coordinate of four. And point π· has an π₯-coordinate of four and a π¦-coordinate of five.

Now under this transformation, what was the π₯-coordinate on the original shape becomes the π¦-coordinate in the transformed shape. And the negative of what was the π¦-coordinate on the original shape becomes the π₯-coordinate on the transformed shape. So if we just write down the coordinates of the four Points π΄, π΅, πΆ, and π· and then weβll apply the transformation to see where they moved to.

Well as we said, what was the π₯-coordinate becomes the new π¦-coordinate. So, for point π΄, the π¦-coordinate will become four. And letβs call the transformed point π΄ dash. For π΅, what was the π₯-coordinate was five will become the π¦-coordinate, and weβll call the transformed point π΅ dashed. The old π₯-coordinate from the original πΆ point becomes the π¦-coordinate in the transformed point πΆ dashed, and the original π₯-coordinate for the π· point becomes the π¦-coordinate for the transformed point π· dashed.

And now we need to transform what was the original π¦-coordinate by taking the negative value and installing that as the π₯-coordinate of the transformed point. So for point π΄, three gets transformed to negative three; for point π΅, the π¦-coordinate of three gets transformed to negative three; for point πΆ, the π¦-coordinate of four gets transformed to negative four; and for point π·, the π¦-coordinate of five gets transformed to the negative of that, negative five, as the π₯-coordinate on the transformed point π· dashed. So we can write down the coordinates of the transformed points π΄ dashed, π΅ dashed, πΆ dashed, and π· dashed in a little answer box there.

Now just before we go, letβs plot those points on our axes over here to see what the transformation looks like. So, π΄ dashed is gonna be a negative three, four, so thatβs up here; π΅ dashed is gonna be a negative three, five, so thatβs up here; πΆ dashed is negative four, five, so thatβs up here; and π· dashed is negative five, four, so thatβs up here.

And joining those points up in the correct order shows us what the transformed figure would look like; itβs a rotation. In fact, itβs a rotation of ninety degrees in the counterclockwise direction about the origin, but since the question didnβt ask that, we donβt have to give that.