Given coordinates of △RST are R(−3, −1) , S(−1, −1) , and T(−4, −5) .
and coordinates of the vertices of △R′S′T′ are R′(1, −2) , S′(1, 0) , and T′(5, −3) .
Solution : We know the rule for the new coordinates of rotatation 90°counterclockwise about the origin.The rule is (h, k) ---> (-k,h).
Where (h,k) are the coordinates of original image on axes and (-k,h) are the coordinates of rotated image.
In resulting coordinates of the image first swap the x and y coordinates of the original image and then make the sign opposite of each x-coordinate.
On applying rule (h, k) ---> (-k,h), we get
R(−3, −1) --> R′(1, -3).
S(−1, −1) --> S′(1, -1).
T(−4, −5) --> T′(5, −4).
Let us apply another rule, each of the y-coordinate is getting reduced by 1 by adding 1 to the new coordinates.
Adding 1 to y-coordinates, we get
(1, -3) --> (1,-3+1) --> R'(1,-2)
(1, -1) --> (1,-1+1) --> S'(1,0) and
(5, −4) --> (5,-4+1) --> T' (5,-3).
So, the transformations steps would be:
1) Translation 1 unit up
2) Rotation of 90 degrees counterclockwise.
