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Question
Find the slope of the line which is perpendicular to `x - y/2 + 3 = 0`
Solution
`x - y/2 + 3 = 0`
`y/2 = x + 3`
y = 2x + 6
Slope of this line = 2
Slope of the line which is perpendicular to the given line
= `(-1)/"Slope of the given line"`
= `(-1)/2`
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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.
