Question

Triangle JKL is reflected across the y-axis.

Which of the following transformations would have moved the triangle to the same quadrant?
a) Dilation of 50%
b) Translations 4 units down
c) 180° rotation around the origin
d) None of the above

Answer 1

A 180° rotation around the origin would move the triangle to the same quadrant as reflecting it across the y-axis. The options of dilation and translation would not move the triangle to a different quadrant horizontally.

Step-by-step explanation:

When a geometric figure such as triangle JKL is reflected across the y-axis, its image appears as if mirrored on the opposite side of the y-axis. The transformations given in the options are dilation, translation, and rotation.

• Dilation of 50% would shrink the triangle to half its size but keep it in the same quadrant, therefore not achieving the same result as reflection across the y-axis.
• Translations 4 units down would move the triangle vertically downward in the coordinate system but would not switch its placement to a different quadrant horizontally.
• 180° rotation around the origin would indeed move the triangle to the same quadrant as a reflection over the y-axis. A 180° rotation turns the figure upside down and also mirrors it across both axes.

Therefore, the correct transformation that would move the triangle to the same quadrant as reflecting it across the y-axis is a 180° rotation around the origin.