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Show that A (-4,-7) , B (-1,2) ,C (8,5) ...

Show that A (-4,-7) , B (-1,2) ,C (8,5) and D (5,-4) are the vertices of a parallelogram.

Text Solution

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`A(-4,-7),B(-1,2),C(8,5)` and `D(5,-4)`
Slope of line `AB=(2-(-7))/(-1-(-4))`
`=(2+7)/(-1+4)=9/3=3`………1
Slope of lines `BC=(5-2)/(8-(-1))`
`=3/9=1/3`…….2
Slope of line `CD=(-4-5)/(5-8)`……….2
Slope of line `CD=(-4-5)/(5-8)`
`=(-9)/(-3)=3`.........3
Slope of line `AD=(-4-(-7))/(5-(-4))`
`=(-4+7)/(5+4)=3/9=1/3`.........4
From 1 and 3
Slope of line `AB+` slope of line CD
`:.` line AB `||` line CD
....(If two lines have equal slopes then they are parallel)
From 2 and 4 .
Slope of line `BC=` slope of line AD.
`:.` line BC `||` line AD.
...(If two lines have equal slopes then they are parallel)
`:.square ABCD` is a parallelogram.
`A(-4,-7),B(-1,2),C(8,5)` and `D(5,-4)` are the vertices of a parallelogram.
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