Question

Triangle XYZ is drawn with vertices X(−2, 4), Y(−9, 3), Z(−10, 7). Determine the line of reflection that produces X′(2, 4).

y = −2
y-axis
x = 4
x-axis

Answer 1

To find the line of reflection that produces X′(2, 4), we need to find the midpoint between X and X′, which is (0, 4).

The line of reflection will be perpendicular to the segment connecting X and X′ and will pass through the midpoint. This segment has a slope of (4-4)/(2-(-2)) = 0, which means the line of reflection is a vertical line passing through (0, 4).

Therefore, the line of reflection is the line given by x = 0, which is the y-axis.