Question

h. triangle pqr is shown on the coordinate grid. a student reflected triangle pqr over the y - axis to create triangle pqr. what rule describes this transformation? k. does this picture show a reflection over the x - axis or a reflection over the y - axis?

Explanation:

Step1: Recall reflection rule over y - axis

For a point $(x,y)$ reflected over the y - axis, the new point is $(-x,y)$. For a triangle with vertices $(x_1,y_1),(x_2,y_2),(x_3,y_3)$, after reflection over the y - axis, the vertices of the new triangle are $(-x_1,y_1),(-x_2,y_2),(-x_3,y_3)$. So the rule for reflecting a figure over the y - axis is $(x,y)\to(-x,y)$.

Step2: Analyze reflection in part K

When a figure is reflected over the x - axis, the x - coordinate remains the same and the y - coordinate changes sign, i.e., $(x,y)\to(x, - y)$. In the picture in part K, the figure is flipped upside - down. The x - values of the corresponding points on the original and reflected figures are the same, and the y - values change sign. So it is a reflection over the x - axis.

Answer:

H. $(x,y)\to(-x,y)$
K. Reflection over the x - axis