Answer:
To rotate Trapezoid TRAP 90 degrees clockwise about the point Y(-1, 3), you can use the following steps:
Translate the trapezoid so that point Y is at the origin (0, 0).
To do this, subtract the coordinates of Y from each point of the trapezoid:
T(2,1) becomes T1(2-(-1), 1-3) = T1(3, -2)
R(5,1) becomes R1(5-(-1), 1-3) = R1(6, -2)
A(8,-4) becomes A1(8-(-1), -4-3) = A1(9, -7)
P(1,-4) becomes P1(1-(-1), -4-3) = P1(2, -7)
Apply a 90-degree clockwise rotation by swapping the x and y coordinates and negating the new x-coordinate:
T1(3, -2) becomes T2(2, 3)
R1(6, -2) becomes R2(2, 6)
A1(9, -7) becomes A2(7, -9)
P1(2, -7) becomes P2(7, -2)
Translate the trapezoid back by adding the coordinates of Y to each point:
T2(2, 3) becomes T(2-(-1), 3+3) = T(3, 6)
R2(2, 6) becomes R(2-(-1), 6+3) = R(3, 9)
A2(7, -9) becomes A(7-(-1), -9+3) = A(8, -6)
P2(7, -2) becomes P(7-(-1), -2+3) = P(8, 1)
Therefore, the trapezoid TRAP with verticals T(2,1), R(5, 1), A(8, -4), and P(1, -4) rotated 90 degrees clockwise about Y(-1, 3) becomes TR'A'P' with verticals T(3, 6), R(3, 9), A(8, -6), and P(8, 1).
Explanation: