Question

triangle pqr has vertices p(-2,-1), q(-1,4), and r(1,3). triangle pqr has vertices p(-2,1), q(-1,-4), and r(1,-3). which transformation maps △pqr onto △pqr, preserving side - lengths so that the triangles are congruent? a. reflection over the x - axis b. reflection over the y - axis c. reflection over the line y = x d. rotation 90° clockwise about the origin e. rotation 180° clockwise about the origin

Explanation:

Step1: Recall reflection rules

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,-y)$.
For point $P(-2,-1)$ in $\triangle PQR$, after reflection over the x - axis, it becomes $P'(-2,1)$. For $Q(-1,4)$, it becomes $Q'(-1, - 4)$ and for $R(1,3)$ it becomes $R'(1,-3)$ which are the coordinates of the vertices of $\triangle P'Q'R'$.

Step2: Analyze other transformations

• Reflection over the y - axis has the rule $(-x,y)$ which is not the case here.
• Reflection over the line $y = x$ has the rule $(y,x)$ which is not applicable.
• A $90^{\circ}$ clock - wise rotation about the origin has the rule $(y,-x)$ which is incorrect.
• A $180^{\circ}$ clock - wise rotation about the origin has the rule $(-x,-y)$ which is not correct for this transformation.

Answer:

A. reflection over the x - axis