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

Below

Explanation:

Got it right.

Answer 2

1 - reflection across tha x-axis;

2 - translation 5 units down;

3 - reflection across the y-axis;

4 - translation 7 units to the right.

Explanation:

1. Consider transformation that maps points A, B, C and D into points E, F, G and H:

• A(-3,4)→E(-3,-4);
• B(1,3)→F(1,-3);
• C(3,6)→G(3,-6);
• D(1,6)→H(1,-6).

Thus, this transformation has a rule

(x,y)→(x,-y).

Points (x,y) and (x,-y) are always placed on the same vertical line symmetrically across the x-axis, so this transformation is a reflection across the x-axis.

2. Consider transformation that maps points A, B, C and D into points E, F, G and H:

• A(-3,4)→E(-3,-1);
• B(1,3)→F(1,-2);
• C(3,6)→G(3,1);
• D(1,6)→(1,1).

This transformation has a rule

(x,y)→(x,y-5)

that is translation 5 units down.

3. Consider transformation that maps points A, B, C and D into points E, F, G and H:

• A(-3,4)→E(3,4);
• B(1,3)→F(-1,3);
• C(3,6)→G(-3,6);
• D(1,6)→H(-1,6).

This transformation has a rule

(x,y)→(-x,y)

and is a reflection across the y-axis.

4. Consider transformation that maps points A, B, C and D into points E, F, G and H:

• A(-3,4)→E(4,4);
• B(1,3)→F(8,3);
• C(3,6)→G(10,6);
• D(1,6)→H(8,6).

This transformation has a rule

(x,y)→(x+7,y)

and is a translation 7 units to the right.