1.

Prove that the points (4, 8), (7, 5) , (1, -1) and (-2, 2) are the vertices of a parallelogram.

Answer» Let the points are `A( 4, 8), B(7, 5), C(1, - 1) and D(-2, 2)`.
` therefore" "AB^(2)=(7-4)^(2)+(5-8 )^(2)=(3)^(2)+(-3)^(2)=9+9=18`
`rArr" "AB=3sqrt(2)`
`" "BC^(2)=(1-7)^(2)+(-1 -5)^(2)=(-6)^(2)+(-6)^(2)= 36+36=72 `
`rArr" "BC=6sqrt(2)`
`" "CD^(2)=(-2-1)^2+(2+1)^(2)=(-3)^(2)+(3)^(2)=9+9=18`
`rArr" " CD=3sqrt(2)`
`" "DA^(2)=(4+2)^(2)+(8-2)^(2)=6^(2)+6^(2)=36+36 =72`
`rArr" "DA=6sqrt(2)`
`because" "AB=CD and BC=DA`


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