Question

Given points: R(-7, -5), S(-1, -2), T(-1, -5). Rotate 90° counterclockwise about the origin. Then translate 3 units left and 8 units up.

a) R'(-5, 4), S(-7, 9), T(-4, 0)
b) R'(5, -4), S(7, -9), T(4, 0)
c) R'(-5, -4), S(-7, -9), T(-4, 0)
d) R'(5, 4), S(7, 9), T(4, 0)

Answer 1

To rotate the points counterclockwise 90° and then translate them left 3 units and up 8 units, we can use the rotation formulas x' = -y and y' = x. The rotated points are R'(-5, 7), S(2, -1), T(5, -1). Then, we translate the points by subtracting 3 from the x-coordinate and adding 8 to the y-coordinate.

Step-by-step explanation:

To rotate a point 90° counterclockwise about the origin, we can use the formulas:

x' = -y

y' = x

Using these formulas, we can find the coordinates of the rotated points:

R'(-5, 7), S(2, -1), T(5, -1)

Then, to translate the points 3 units left and 8 units up, we subtract 3 from the x-coordinate and add 8 to the y-coordinate:

R'(-8, 15), S(-1, 7), T(2, 7)