Question

Line SK has coordinates S(-1,-8) and K(1, 2). The segment is translated over 3 to the right and up 3 to form S'K'. S'K' is rotated about the origin 90°CCW to form S'K". What are the coordinates of S'K' and S' K"?​

Answer 1

After translating S(-1,-8) and K(1, 2) by 3 units to the right and up, the coordinates of S'K' are S'(2,-5) and K'(4, 5). After rotating S'K' 90° CCW about the origin, the coordinates of S"K" are S"(-5,-2) and K"(-5,4).

Step-by-step explanation:

First, let's find the coordinates of S'K' after the translation. To translate line SK to the right by 3 units and up by 3 units, we add 3 to each x-coordinate and to each y-coordinate of S(-1,-8) and K(1, 2). This gives us S'(2,-5) and K'(4, 5).

Next, the rotation of S'K' about the origin 90° counterclockwise can be achieved by applying the transformation rules for 90° rotation, which are x' = -y and y' = x. Applying these to S'(2,-5) we get S"(-5,-2) and for K'(4, 5) we get K"(-5,4).

In summary, after the translation and rotation, the coordinates of S'K' are S'(2,-5) and K'(4, 5), and for S"K" are S"(-5,-2) and K"(-5,4).