Question

In the diagram shown below, triangle ABC is drawn along with point D.(a) Plot triangle A'B'C', the image of triangle ABC after a clockwise rotation of 90 degrees about Point D. Give the coordinates of the new vertices below.

Answer 1

First of all, it is necessary to translate the origin of coordinates to the center of rotation, which is the point (1,-3), it means it is necessary to move the origin 1 unit right and 3 units down.

In order to find the new figure after the rotationof 90°, take into account the following transformations:

T(x,y) => (y,-x)

where x' and y' are the new coordinates of a point.

x and y are the vertical and horizontal distance to the origin, then, you obtain:

A(-7,9) => A''(9,7)

B(-7,4) => B''(4,7)

C(-3,4) => C''(4,3)

Next, it is necessary to subtract or add the units of the initial translation (1 unit right and 3 units down):

A'(9+1,7-3) => A'(10,4)

B'(4+1,7-3) => B'(5,4)

C'(4+1, 3-3) => C'(5,0)