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Question
Find k, if R(1, –1), S (–2, k) and slope of line RS is –2.
Solution
Slope of line RS is –2
Slope of RS will be
\[\frac{y_2 - y_1}{x_2 - x_1} = \frac{k - \left( - 1 \right)}{- 2 - 1} = \frac{k + 1}{- 3} = - 2\]
\[ \Rightarrow k + 1 = 6\]
\[ \Rightarrow k = 5\]
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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.
