Question

Figure 1 and Figure 2 are two congruent parallelograms drawn on a coordinate grid as shown.
4-quadrant coordinate grid showing two parallelograms. Figure 1 has vertices at (-5, 3) , (-3, 5), (-4, 8), and (-6,6). Figure 2 has vertices at (5, -7), (3, -5), (4, -2), and (6, -4).

Which two transformations can map Figure 1 onto Figure 2?. .

A.) reflection across the y-axis followed by translation 10 units down
B.) reflection across the y-axis followed by reflection across x-axis
C.) reflection across the y-axis followed by translation 5 units down
D.) reflection across the x-axis followed by reflection across y-axis

Answer 1

The correct answer is:

A) reflection across the y-axis followed by translation 10 units down

Explanation:

Reflecting across the y-axis negates the x-coordinate of each point. This maps our points as follows:

(-5, 3)→(5, 3)

(-3, 5)→(3, 5)

(-4, 8)→(4, 8)

(-6, 6)→(6, 6)

A translation 10 units down will subtract 7 from each y-coordinate. This maps our new points as follows:

(5, 3)→(5, 3-10) = (5, -7)

(3, 5)→(3, 5-10) = (3, -5)

(4, 8)→(4, 8-10) = (4, -2)

(6, 6)→(6, 6-10) = (6, -4)

This is the correct set of image points, so this is the correct set of transformations.

Answer 2

Answer:

A) reflection across the y-axis followed by translation 10 units down

Step-by-step explanation: