Question

Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD. E(-3, -4), F(1, -3), G(3, -6), and H(1, -6) a translation 7 units right E(-3, -1), F(1, -2), G(3, 1), and H(1, 1) a reflection across the y-axis E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6) a reflection across the x-axis E(4, 4), F(8, 3), G(10, 6), and H(8, 6) a translation 5 units down

Answer 1

A translation 7 units right --> E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

Reflection across y-axis --> E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

Reflection across x-axis --> E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

A translation 5 unit down --> E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

Answer 2

Match: a translation 7 units right = > E(4, 4), F(8, 3), G(10, 6), and H(8, 6)

Match: Reflection across y-axis = > E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

Match: Reflection across x-axis = > E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

Match: a translation 5 unit down = > E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)

A) translation 7 unit Right. In this reflection x-coordinate shift 7 unit right.

`T(x,y)\rightarrow T(x+7,y)`

B) Reflection across y-axis. In this reflection x value change their sign.

`R(x,y)\rightarrow R(-x,y)`

Match: Reflection across y-axis = > E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)

C) Reflection across x-axis. In this reflection y value change their sign.

`R(x,y)\rightarrow R(x,-y)`

Match: Reflection across x-axis = > E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)

D) a translation 5 unit down. In this translation y-coordinate will shift 5 unit down.

`T(x,y)\rightarrow T'(x,y-5)`

Match: a translation 5 unit down = > E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)