Question

The vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A′B′C′D′. Match each vertex of polygon A′B′C′D′ to its coordinates.

Tiles
(2, 1)
A′
(1, 1)
B′
(3, 0)
C′
(2, 3)
D′
(-3, 4)
(2, -1)
(-2, 5)

Answer 1

Answer: The required match is given by

A' (1, 1)

B' (2, -1)

C' (3, 0)

D' (2, 1).

Step-by-step explanation: Given that the vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1).

ABCD is reflected across the x-axis and translated 2 units up to form polygon A′B′C′D′.

We are to match the vertices of polygon ABCD to its co-ordinates.

We know that

if a point (x, y) is reflected across X-axis, hen the sign before the y co-ordinate changes. Also, if there is an additional translation of 2 units up, then the required transformation will be

(x, y) ⇒ (x, -y + 2).

So, after getting reflected across the X-axis, the co-ordinates of the vertices of ABCD will change as follows :

A(1, 1) ⇒ A'(1, -1+2) = A'(1, 1)

B(2, 3) ⇒ B'(2, -3+2) = B'(2, -1)

C(3, 2) ⇒ C'(3, -2+2) = C'(3, 0)

and

D(2, 1) ⇒ D'(2, -1+2) = D'(2, 1).

Thus, the required match is given by

A' (1, 1)

B' (2, -1)

C' (3, 0)

D' (2, 1).

Answer 2

The vertices of polygon ABCD are at A(1, 1), B(2, 3), C(3, 2), and D(2, 1). ABCD is reflected across the x-axis and translated 2 units up to form polygon A′B′C′D′. Match each vertex of polygon A′B′C′D′ to its coordinates.Tiles
(2, 1)A′(2, -1)
(1, 1)B′(-3, 4)
(3, 0)C′(2, -1)
(2, 3)D′(-2, 5)