Question

Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if Z′(10, 8).

y = 1

x = −8

y-axis

x-axis

Answer 1

(d) x-axis

Explanation:

Answer 2

(d) x-axis

Explanation:

You want the line of reflection that transforms Z(10, -8) to Z'(10, 8).

Line of reflection

The line of reflection is the perpendicular bisector of the segment between a point and its image.

Here, the segment ZZ' is on the vertical line x=10, so the bisector will be a horizontal line whose y-value is the average of the y-values of Z and Z':

y = (-8 +8)/2 = 0/2 = 0

The line y=0 is the x-axis. The line of reflection is the x-axis.

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Additional comment

Rather than go to the trouble of considering perpendicular bisectors, you can simply make use of your knowledge of reflection over the axes:

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

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

(x, y) ⇒ (-x, -y) . . . . reflection over both axes, or reflection across the origin