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)

Answer 1

here is the answer

Explanation:

Answer 2

The set of vertices of quadrilateral EFGH with the transformation 7 units right is E(4 , 4) , F(8 , 3) , G(10 , 6) , and H(8 , 6)

The set of vertices of quadrilateral EFGH with a reflection across the y-axis is E(3 , 4) , F(-1 , 3) , G(-3 , 6) , and H(-1 , 6)

The set of vertices of quadrilateral EFGH with a reflection across the x-axis is E(-3 , -4) , F(1 , -3) , G(3 , -6) , and H(1 , -6)

Explanation:

Lets revise some transformation

- If point (x , y) reflected across the x-axis

then Its image is (x , -y)

- If point (x , y) reflected across the y-axis

then Its image is (-x , y)

- If the point (x , y) translated horizontally to the right by h units

then its image is (x + h , y)

- If the point (x , y) translated horizontally to the left by h units

then its image is (x - h , y)

* Now lets solve the problem

- The vertices of the quadrilateral ABCD are:

A = (-3 , 4) , B = (1 , 3) , C = (3 , 6) , D = (1 , 6)

- The quadrilateral ABCD translated 7 units right to form

quadrilateral EFGH

- We add each x-coordinates in ABCD by 7

∵ A = (-3 , 4)

∴ E = (-3 + 7 , 4) = (4 , 4)

∵ B = (1 , 3)

∴ F = (1 + 7 , 3) = (8 , 3)

∵ C = (3 , 6)

∴ G = (3 + 7 , 6) = (10 , 6)

∵ D = (1 , 6)

∴ H = (1 + 7 , 6) = (8 , 6)

* The set of vertices of quadrilateral EFGH with the transformation

7 units right is E(4 , 4) , F(8 , 3) , G(10 , 6) , and H(8 , 6)

- The quadrilateral ABCD reflected across the y-axis to form

quadrilateral EFGH

- We change the sign of the x-coordinate

∵ A = (-3 , 4)

∴ E = (3 , 4)

∵ B = (1 , 3)

∴ F = (-1 , 3)

∵ C = (3 , 6)

∴ G = (-3 , 6)

∵ D = (1 , 6)

∴ H = (-1 , 6)

* The set of vertices of quadrilateral EFGH with a reflection across the

y-axis is E(3 , 4) , F(-1 , 3) , G(-3 , 6) , and H(-1 , 6)

- The quadrilateral ABCD reflected across the x-axis to form

quadrilateral EFGH

- We change the sign of the y-coordinate

∵ A = (-3 , 4)

∴ E = (-3 , -4)

∵ B = (1 , 3)

∴ F = (1 , -3)

∵ C = (3 , 6)

∴ G = (3 , -6)

∵ D = (1 , 6)

∴ H = (1 , -6)

* The set of vertices of quadrilateral EFGH with a reflection across the

x-axis is E(-3 , -4) , F(1 , -3) , G(3 , -6) , and H(1 , -6)