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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.

In the diagram shown below triangle ABC is drawn along with point Da Plot triangle ABC the image of triangle ABC after a clockwise rotation of 90 degrees about class=

Respuesta :

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)

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