Answer:
Reflection across the x-axis, followed by translation 10 units right.
Step-by-step explanation:
I'm sorry, I know the question asks for two transformations, but let's look a the math before tackling the figure (see attachment).
When you are asked to do a reflection on the x-axis, they are asking you to invert the sign on the y coordinate of every point, and when you are asked to do a reflection on the y-axis, just invert the sign of the x coordinate, always following the convention of (x, y).
Translation to the right means to add the amount of units given to all the x coordinates, to the left means to subtract said number of units.
Translation down is to subtract those units to the y coordinate and translation up, is to add to that y coordinate.
So in this exercise:
Fig 1 coordinates are:
(-5, 2) (-3, 4) (-4, 7) (-6, 5)
Fig 2 coordinates are:
(5, -2) (7, -4) (6, -7) (4, -5)
So let's test the options given:
a. Reflection across the y-axis, followed by reflection across x-axis
Reflection across the y-axis:
Fig 1.1: (5, 2) (3, 4) (4, 7) (6, 5) <- Every x coordinate with inverted sign
Then reflection across x-axis:
Fig 1.2: (5, -2) (3, -4) (4, -7) (6, -5) <- Every y coordinate with inverted sign
if we compare this new Fig 1.2 with Fig 2:
(5, -2) (3, -4) (4, -7) (6, -5) ≠ (5, -2) (7, -4) (6, -7) (4, -5) Wrong
b. Reflection across the x-axis, followed by reflection across y-axis
Reflection across the x-axis:
Fig 1.1: (-5, -2) (-3, -4) (-4, -7) (-6, -5) <- Every y coordinate with inverted sign
Then reflection across y-axis:
Fig 1.2: (5, -2) (3, -4) (4, -7) (6, -5) <- Every x coordinate with inverted sign
if we compare this new Fig 1.2 with Fig 2:
(5, -2) (3, -4) (4, -7) (6, -5) ≠ (5, -2) (7, -4) (6, -7) (4, -5) Wrong
c. Reflection across the x-axis, followed by translation 10 units right
Reflection across the x-axis:
Fig 1.1: (-5, -2) (-3, -4) (-4, -7) (-6, -5) <- Every y coordinate with inverted sign
Then translation 10 units right:
Fig 1.2: (5, -2) (7, -4) (6, -7) (4, -5) <- Every x coordinate +10
if we compare this new Fig 1.2 with Fig 2:
(5, -2) (7, -4) (6, -7) (4, -5) = (5, -2) (7, -4) (6, -7) (4, -5) Correct!
d. Reflection across the y-axis, followed by translation 5 units down
Reflection across the y-axis:
Fig 1.1: (5, 2) (3, 4) (4, 7) (6, 5) <- Every x coordinate with inverted sign
Then translation 5 units down:
Fig 1.2: (5, -3) (3, -1) (4, 2) (6, 0) <- Every y coordinate -5
if we compare this new Fig 1.2 with Fig 2:
(5, -3) (3, -1) (4, 2) (6, 0) ≠ (5, -2) (7, -4) (6, -7) (4, -5) Wrong
So from all options only c. works
