Answer:
A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces Δ X'Y'Z' from Δ XYZ
Step-by-step explanation:
* Lets revise the rotation and translation
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 180° anti-clock wise
∴ Its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° anti-clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180° clock wise
∴ Its image is (-x , -y)
- If point (x , y) rotated about the origin by angle 270° clock wise
∴ Its image is (-y , x)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is = (x , y - k)
* Now lets solve the problem
- Δ XYZ has vertices X = (-5 , 3) , Y = (-2 , 3) , Z = (-2 , 1)
∵ Δ XYZ rotate 90° clockwise about the origin the image will be (y , -x)
∴ The image of X is (3 , 5)
∴ The image of Y is (3 , 2)
∴ The image of Z is (1 , 2)
- From the graph
∵ X' = (5 , -1)
∵ Y' = (5 , -4)
∵ Z' = (3 , -4)
- Every x-coordinate add by 2
∴ There is a translation 2 units to the right
- Every y-coordinate subtracted by 6
∴ There is a translation 6 units down
- From all above
* A clockwise rotation 90° about the origin followed by a translation
2 units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ
