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प्रश्न
Find the slope of a line passing through the given pair of points (3,7) and (5,13)
उत्तर
Slope of line = `("y"_2 - "y"_1)/("x"_2 - "x"_1)`
= `(13 - 7)/( 5 - 3)`
= 3
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संबंधित प्रश्न
The side AB of an equilateral triangle ABC is parallel to the x-axis. Find the slopes of all its sides.
The side AB of a square ABCD is parallel to the x-axis. Find the slopes of all its sides. Also, find:
- the slope of the diagonal AC.
- the slope of the diagonal BD.
The slope of the side BC of a rectangle ABCD is `2/3`. Find:
- the slope of the side AB.
- the slope of the side AD.
Find the slope and the inclination of the line AB if : A = `(0, - sqrt(3))` and B = (3, 0)
Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.
90°
Find the slope of the lines passing through the given point.
P (–3, 1) , Q (5, –2)
Find the value, of k, if the line represented by kx – 5y + 4 = 0 and 4x – 2y + 5 = 0 are perpendicular to each other.
Show that the points A(- 2, 5), B(2, – 3) and C(0, 1) are collinear.
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.
