# Question Video: Sketching the Image of a Transformation After a Given Coordinate Transformation Mathematics

The given figure shows a triangle on the coordinate plane. Sketch the image of the triangle after the geometric transformation (π₯, π¦) βΆ (βπ¦, π₯).

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### Video Transcript

The given figure shows a triangle on the coordinate plane. Sketch the image of the triangle after the geometric transformation π₯, π¦ is mapped to negative π¦, π₯.

We are told that the geometric transformation we need to apply is at a general point with coordinates π₯, π¦ is mapped to the point with coordinates negative π¦, π₯. This means that the π₯- and π¦-coordinates swap around, and then we also change the sign of the new π₯-coordinate. We can apply this mapping to the coordinates of each vertex of triangle π΄π΅πΆ individually.

The coordinates of vertex π΄ are two, four. Applying the given mapping, so swapping the coordinates around and then changing the sign of the new π₯-coordinate, gives the point π΄ prime with coordinates negative four, two. We can plot this point on the coordinate grid to show the image of point π΄. The coordinates of point π΅ are three, one. Applying the given mapping gives the coordinates of π΅ prime as negative one, three, and then we can also plot this point. Finally, the coordinates of point πΆ are one, one, which under the given transformation is mapped to negative one, one. Plotting point πΆ prime and then connecting the three points together gives the image of triangle π΄π΅πΆ after the given transformation.

Although it isnβt required, we can also observe that the type of transformation that has been applied is a rotation, because the orientation of the triangle has changed: itβs now on its side compared to its original orientation.