Question

Plot points K = (0,0), L = (7, -1), M = (9,3), P = (6,7), Q = (10,5), and R = (1,2). Show that the triangles KLM and RPQ are congruent. Show also that neither triangle is a vector translation of the other. Describe how one triangle has been transformed into the other. Draw a diagram.

Answer 1

`\begin{gathered} \text{ To show that triangles KLM and RPQ are congruent, we have to show that} \\ KL=RP, \\ LM=PQ \\ MK=QR \\ \text{Solve for KL and RP} \\ KL=√((7 - 0)^2 + (-1 - 0)^2)=\sqrt[]{50} \\ RP=√((6 - 1)^2 + (7 - 2)^2)=\sqrt[]{50} \\ \text{Solve for LM and PQ} \\ LM=√((9 - 7)^2 + (3 - (-1))^2)=\sqrt[]{20} \\ PQ=√((10 - 6)^2 + (5 - 7)^2)=\sqrt[]{20} \\ \text{Solve for MK and QR} \\ MK=√((0 - 9)^2 + (0 - 3)^2)=\sqrt[]{90} \\ QR=√((1 - 10)^2 + (2 - 5)^2)=\sqrt[]{90} \\ \text{All of the corresponding sides are equal in measurement, therefore triangle KLM} \\ \text{and RPQ are congruent} \end{gathered}`