Question

X

Intro
Y
N
y
N
Z'
x
X'
Y'
Complete the sequence of transformations that
produces AXY'Z' from AXYZ.
A clockwise rotation
by a translation
about the origin followed
units to the right and 6 units down
produces AX'Y'Z' from AXYZ.
Done

Answer 1

• clockwise 90°
• right 2 units

Explanation:

You want to identify the amount of clockwise rotation and translation that maps XYZ to X'Y'Z' given the graphs of the two figures.

Clockwise rotation

A rotation 90° clockwise is represented by the transformation ...

(x, y) ⇒ (y, -x)

In the given figures, segment XY points east, and segment X'Y' points south. A clockwise rotation of 90° will change the facing direction from east to south.

The clockwise rotation is 90°.

Translation

Using the above transformation, the rotated position of point X would be ...

X(-5, 3) ⇒ X"(3, 5)

We note that the actual position of point X' is (5, -1). To get from the rotated position to the final position requires a translation right h units and down 6 units:

X' = X" +(h, -6)

(5, -1) = (3, 5) +(h, -6) = (3+h, 5 -6)

Matching x-coordinates, we have ...

5 = 3+h ⇒ h = 2 . . . . . . . the translation right is 2 units