A triangle has vertices W(−3,7) , Q(1,−1) , and Z(−5,−2) . Apply rotation mapping rules to find the coordinates of W′ after a 90-degree (counterclockwise) rotation about the origin.(1 point)
To rotate a point 90 degrees counterclockwise about the origin, we can use the following rotation mapping rules:
x' = x * cos(90°) - y * sin(90°)
y' = x * sin(90°) + y * cos(90°)
Substituting the values of the point W(-3,7), we get:
x' = -3 * cos(90°) - 7 * sin(90°)
y' = -3 * sin(90°) + 7 * cos(90°)
Since cos(90°) = 0 and sin(90°) = 1, we have:
x' = -3 * 0 - 7 * 1 = -7
y' = -3 * 1 + 7 * 0 = -3
Hence, the coordinates of W' after a 90-degree counterclockwise rotation about the origin are W'(-7,-3).