Question

the vertices for two triangles are given.
the coordinates of the vertices of the first triangle are r (-4,6), s (-1,2) and t (-6,-1).
the coordinates of the vertices of the second triangle are l (6,-4), m (-1,-6), n (2,-1).
which statement describes the relationship between the first and second triangles?
which expression relates the first triangle to the second?
a. △rst≅△lnm/(x,y)→(y,x)
b. △rts≅△mln/(x,y)→(x,-y)
c. △rst - △lnm/(x,y)→(-x,y)
d. △rts - △mln/(x,y)→(-y,-x)

Explanation:

Step1: Recall congruence and transformation rules

Congruent triangles have same shape and size. Transformations like reflections, rotations, translations can relate them. Analyze each transformation rule in options.

Step2: Check option A

For $\triangle{RST}$ with vertices $R(-4,6),S(-1,2),T(-6, - 1)$ and transformation $(x,y)\to(y,x)$. For $R(-4,6)$ it becomes $(6,-4)$ which is $L$. For $S(-1,2)$ it becomes $(2,-1)$ which is $N$. For $T(-6,-1)$ it becomes $(-1,-6)$ which is $M$. And $\triangle{RST}\cong\triangle{LNM}$ as the vertices match after the transformation.

Step3: Check option B

For transformation $(x,y)\to(x, - y)$, for $R(-4,6)$ it becomes $(-4,-6)$ which does not match any vertex of the second - triangle.

Step4: Check option C

For transformation $(x,y)\to(-x,y)$, for $R(-4,6)$ it becomes $(4,6)$ which does not match any vertex of the second - triangle.

Step5: Check option D

For transformation $(x,y)\to(-y,-x)$, for $R(-4,6)$ it becomes $(-6,4)$ which does not match any vertex of the second - triangle.

Answer:

A. $\triangle{RST}\cong\triangle{LNM}/(x,y)\to(y,x)$