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Show that the points A(-3, 3), B(7, -2) ...

Show that the points `A(-3, 3), B(7, -2) and C(1,1) ` are collinear.

Text Solution

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` " "AB =sqrt((7+3)^(2)+(-2-3)^(2))=sqrt((10)^(2)+(-5)^(2) )`
` " "=sqrt(100+25)=sqrt(125)=5sqrt(5)`
` " "BC=sqrt((1-7)^(2)+(1+2)^(2))=sqrt((-6)^(2) +(3)^(2))`
`" "=sqrt(36+9)=sqrt(45)=3sqrt(5)`
and `" " AC=sqrt((1+3)^(2)+(1-3)^(2))=sqrt((4)^(2)+(-2)^(2))`
` " "=sqrt(16 +4)=sqrt(20)=2sqrt(5)`
Now, `" "AC+B C=2sqrt(5)+3sqrt(5)=5sqrt(5)=AB`
` therefore` Points A, B and C are collinear.
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