MATH SOLVE

4 months ago

Q:
# ASAP GUYS!!!! (I NEED TO FINISH THIS QUICK) Graph Complete the sequence of transformations that produces △X'Y'Z' from △XYZ. A clockwise rotation °______ about the origin followed by a translation ______ units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.

Accepted Solution

A:

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 XYZStep-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