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Algebra
Pregunta

Quadrilateral \(R S T U\) has vertices at \(R ( 1,...

Quadrilateral \(R S T U\) has vertices at \(R ( 1,11 ) , S ( 9,12 ) , T ( 13,5 )\) and \(U ( 2 , - 2 )\) . 

(a) Show that the diagonals of \(R S T U\) are perpendicular. 

(b) Show that \(\overline { R S } \cong \overline { S T }\) 

Answer

(a)The polygon is drawn as follows:

The slope of RT is \(k_{1}= - \frac{1}{2}\),and the slope of SU is \(k_{2}= 2\).

\(k_{1}k_{2}= - 1\)

(b)\(RS= \sqrt{8^{2}+ 1}= \sqrt{65}\)

\(ST= \sqrt{4^{2}+ (- 7)^{2}}= \sqrt{65}\)

so \(RS= ST\)

Solución
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