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Question
Find the slope of a line passing through the point A (-2,1), B (0,3).
Solution
`"Slope of a line passing through 2 points "(x_1, "y"_1) " and "(x_1,"y"_1)=(("y"_2-"y"_1)/(x_2-x_1))`
`"Slope of a line passing through 2 points (-2, 1) and (0, 3)"=((3-1)/(0+2))=2/2=1`
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Solution:
Slope of line = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
∴ Slope of line AB = `(2 - 1)/(8 - 6) = square` .......(i)
∴ Slope of line BC = `(4 - 2)/(9 - 8) = square` .....(ii)
∴ Slope of line CD = `(3 - 4)/(7 - 9) = square` .....(iii)
∴ Slope of line DA = `(3 - 1)/(7 - 6) = square` .....(iv)
∴ Slope of line AB = `square` ......[From (i) and (iii)]
∴ line AB || line CD
∴ Slope of line BC = `square` ......[From (ii) and (iv)]
∴ line BC || line DA
Both the pairs of opposite sides of the quadrilateral are parallel.
∴ `square`ABCD is a parallelogram.
