Question

Coordinate R (1,5) S (6,-1) and T (1,-4) are connected to form ∆ RST if ∆ RST is congruent to ∆ RWT what are the coordinates of W

Answer 1

The triangles are similar, then ratio of corresponding sides of triangle are equal. The ratio of corresponding sides of two triangle RST and triangle RWT is,

$\begin{gathered} \frac{RS}{RW}=\frac{RT}{RT} \\ \frac{RS}{RW}=1 \\ RS=RW \end{gathered}$

Determine the length of side RS.

$\begin{gathered} RS=\sqrt[]{(1-6)^2+(5+1)^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}$

So the distance between point RW is also equal to square root 61.

For option (-4,2),

$\begin{gathered} RW=\sqrt[]{(-4-1)^2+(5-2)} \\ =\sqrt[]{25+9} \\ =\sqrt[]{36} \end{gathered}$

For o(-6,-1),

$\begin{gathered} RW=\sqrt[]{(-6-1)^2+(5+1)^2} \\ =\sqrt[]{49+36} \\ =\sqrt[]{85} \end{gathered}$

For (-4,-1),

$\begin{gathered} RW=\sqrt[]{(1+4)^2+(5+1)^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}$

So coordinate of point W is (-4,-1) as it give same distance of RS and RW.

Answer: (-4,-1)