Question

Point A, located at (-11,17) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C. What are coordinates of points B and C?

Answer 1

B = (-11, -17)

C = (11, -17)

Explanation:

Reflection over the x-axis is accomplished by changing the sign of the y-coordinate:

(x, y) ⇒ (x, -y) . . . . . reflection over x-axis

Reflection over the y-axis is accomplished by changing the sign of the x-coordinate:

(x, y) ⇒ (-x, y) . . . . . reflection over the y-axis

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B = (-11, -17)

C = (11, -17)

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Check

Reflection over both axes negates both coordinates. It is equivalent to reflection over the origin, or rotation 180°.

A(-11, 17) ⇒ C(11, -17) . . . . . both coordinates change sign