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Sagot :
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,
[tex]\begin{gathered} \frac{RS}{RW}=\frac{RT}{RT} \\ \frac{RS}{RW}=1 \\ RS=RW \end{gathered}[/tex]Determine the length of side RS.
[tex]\begin{gathered} RS=\sqrt[]{(1-6)^2+(5+1)^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}[/tex]So the distance between point RW is also equal to square root 61.
For option (-4,2),
[tex]\begin{gathered} RW=\sqrt[]{(-4-1)^2+(5-2)} \\ =\sqrt[]{25+9} \\ =\sqrt[]{36} \end{gathered}[/tex]For o(-6,-1),
[tex]\begin{gathered} RW=\sqrt[]{(-6-1)^2+(5+1)^2} \\ =\sqrt[]{49+36} \\ =\sqrt[]{85} \end{gathered}[/tex]For (-4,-1),
[tex]\begin{gathered} RW=\sqrt[]{(1+4)^2+(5+1)^2} \\ =\sqrt[]{25+36} \\ =\sqrt[]{61} \end{gathered}[/tex]So coordinate of point W is (-4,-1) as it give same distance of RS and RW.
Answer: (-4,-1)
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