Question : What is the reflection of the point (5, 3) in the line $y = –2$?
Option 1: (– 9, 3)
Option 2: (– 5, – 7)
Option 3: (– 9, – 3)
Option 4: (5, – 7)
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Correct Answer: (5, – 7)
Solution :
Given:
The point (5, 3) and the line $y$ = –2.
We know that the only coordinate that changes when a point is reflected on the x-axis is the $y$ coordinate.
The line $y$ = –2 is perpendicular to the x-axis and the reflection will not change the $x$ coordinate.
The distance between the reflected point and the line will now equal the distance between the original point and the line along the y-direction.
The $y$ direction distance between a point and a line equals $|3–(–2)|=5$ unit.
The $y$ coordinate of reflection equals –2–5 = –7
The reflection point is (5, –7).
Hence, the correct answer is (5, –7).
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