Question

Y

A
B
4
Analyze the pre-image ABCD. What are the vertices of
the final image if T_1,-2y = x is applied to figure
ABCD?
A"
B"(3, 2)
C"
D"
2
D
с
<
*
-2
-2

Answer 1

A"(3, 0), B"(3, 2), C"(1, 1), D"(1, -1)

Explanation:

Coordinates of A,B,C and D are,

A(2, 4), B(4, 4), C(3, 2) and D(1, 2)

Rule for the reflection over a line y = x,

(x, y) → (y, x)

Therefore, new image of ABCD will be,

A(2, 4) → A'(4, 2)

B(4, 4) → B'(4, 4)

C(3, 2) → C'(2, 3)

D(1, 2) → D'(2, 1)

Rule for translation
`T_(-1, -2)`,

(x, y) → (x - 1, y - 2)

By this rule image of A'B'C'D' will be,

A'(4, 2) → A"(3, 0)

B'(4, 4) → B"(3, 2)

C'(2, 3) → C"(1, 1)

D'(2, 1) → D"(1, -1)