Question

Triangle RST and its image, triangle R’S’T’, are graphed on the coordinate grid below. On a coordinate plane, triangle R S T has points (0, 1), (negative 2, 2), (negative 1, 4). Triangle R prime S prime T prime has points (1, 0), (2, 2), (4, 1). Which rotation, using the origin as the center of rotation, transformed RST to R’S’T’? a 90° clockwise rotation a 90° counterclockwise rotation a 45° clockwise rotation a 45° counterclockwise rotation

Answer 1

Given:

The coordinates of the triangle RST are (0,1), (-2,2) and (-1,4)

The coordinates of the triangle R'S'T' are (1,0), (2,2) and (4,1)

We need to determine the rotation about origin.

Rotation about the origin:

To determine the rotation about the origin, we need to find the translation rule.

The coordinates of the point R to R' is
`R(0,1)\implies R'(1,0)`

The translation rule for the point R to R' is
`(x,y)\implies (y,-x)`

The coordinate of the point S to S'is
`S(-2,2)\implies S'(2,2)`

The translation rule for the point S to S' is
`(x,y)\implies (y,-x)`

The coordinates of the point T to T' is
`T(-1,4)\implies T'(4,1)`

The translation rule for the point T to T' is
`(x,y)\implies (y,-x)`

Therefore the rule to translate the triangle RST to R'S'T' is
`(x,y)\implies (y,-x)`

Hence, the triangle is rotated 90° clockwise about the origin.

Hence, Option a is the correct answer.