Answer:
The Transformations are R(O , -90°) & R(O , 270)
Explanation:
* Lets revise the rotation of a point
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clock wise
(270° anti-clockwise or -90°)
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise (-180°) or
anti-clockwise (180°) around the origin
* Lets solve the problem
∵ One vertex of a triangle is located at (0, 5) on a coordinate grid
∵ The image of the point after the transformation is (5 , 0)
- The coordinates are switched with each other
∴ There is no rotation with 180° or -180° because in the rotation with
180° and -180° around the origin we change only the signs of the
coordinates without switch them
∴ There is a rotation with 90° are 270° or -90°
- The zero has no sign
- When we rotate the point (0 , 5) by -90° or 270° around the origin
we will change the sign of x-coordinate and switch the two
coordinates
∴ The image of the point is (y , -x)
∵ x = 0 and y = 5
- There is no sign for zero, so we switch the coordinates only
∴ The vertex is located at (5, 0)
∴ The Transformations are R(O , -90°) & R(O , 270)