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प्रश्न
Find slope of a line passing through the points A(3, 1) and B(5, 3).
उत्तर
A ≡ (3, 1) ≡ (x1 , y1) and B ≡ (5, 3) ≡ (x2 , y2)
Slope of a line AB = `(y_2 - y_1)/(x_2 - x_1)`
`= (3-1)/(5-3)`
= `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.
