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प्रश्न
Determine x so that the slope of the line through (1, 4) and (x, 2) is 2.
उत्तर
Given, the slope of the line through (1, 4) and (x, 2) is 2.
∴ `(2 -4)/(x -1)=2`
`(-2)/(x - 1) = 2`
`(-1)/(x - 1) = 1`
–1 = x – 1
x = 0
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संबंधित प्रश्न
Find the slope of the line passing through the points A(2, 3) and B(4, 7).
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Determine whether the following point is collinear.
D(–2, –3), E(1, 0), F(2, 1)
Find k, if R(1, –1), S (–2, k) and slope of line RS is –2.
Fill in the blank using correct alternative.
A line makes an angle of 30° with the positive direction of X– axis. So the slope of the line is ______.
Find m if the slope of the line passing through the point (-7,5) and (2,m) is `1/3`
If A(6, 1), B(8, 2), C(9, 4) and D(7, 3) are the vertices of `square`ABCD, show that `square`ABCD is a parallelogram.
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.
Show that points A(– 4, –7), B(–1, 2), C(8, 5) and D(5, – 4) are the vertices of a parallelogram ABCD
Find the slope of the line passing through given points G(3, 7) and K(–2, –3).
