How do you use the distance formula to calculate the lengths of the side of a triangle with vertices #P(5,0), Q(-3,-4), R(-7,4)#?

1 Answer
Jim G.
Feb 12, 2018

#"see explanation"#

Explanation:

#"using the "color(blue)"distance formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))#

#PQ=sqrt((-3-5)^2+(4-0)^2)#

#color(white)(PQ)=sqrt(64+16)=sqrt80=4sqrt5#

#QR=sqrt((-7+3)^2+(4+4)^2)#

#color(white)(QR)=sqrt(16+64)=sqrt80=4sqrt5#

#PR=sqrt((-7-5)^2+(4-0)^2)#

#color(white)(PR)=sqrt(144+16)=sqrt160=4sqrt10#

#"since "PQ=QR" triangle is isosceles"#

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