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Question
Determine whether the given point is collinear.
L(1,2), M(5,3) , N(8,6)
Solution
L(1,2), M(5,3) , N(8,6)
Slope of LM
\[= \frac{3 - 2}{5 - 1} = \frac{1}{4}\]
Slope of MN = \[\frac{6 - 3}{8 - 5} = \frac{3}{3} = 1\]
Thus, the slope of LM not equal to slope MN.
So, the given points are not collinear.
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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.
If the lines 7y = ax + 4 and 2y = 3 − x, are parallel to each other, then the value of ‘a’ is:
