Advertisements
Advertisements
प्रश्न
Find the slope of the line passing through the points G(4, 5) and H (–1, –2).
उत्तर
The slope of the line passing through the points
APPEARS IN
संबंधित प्रश्न
The slope of a line joining P(6, k) and Q(1 – 3k, 3) is `1/2`. Find:
- k.
- mid-point of PQ, using the value of ‘k’ found in (i).
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.
The points (−3, 2), (2, −1) and (a, 4) are collinear. Find a.
Lines 2x – by + 5 = 0 and ax + 3y = 2 are parallel to each other. Find the relation connecting a and b.
If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.
Angle made by the line with the positive direction of X-axis is given. Find the slope of the line.
45°
Angles made by the line with the positive direction of X–axis is given. Find the slope of these line.
60°
Find the slope of the lines passing through the given point.
A(2, 3), B(4, 7)
Find the slope of the lines passing through the given point.
P (–3, 1) , Q (5, –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 the slope of a line, correct of two decimals, whose inclination is 60°
Find the slope of the line passing through the points M(4,0) and N(-2,-3).
Find the slope of the line passing through the points A(4,7) and B(2,3).
Given that (a, 2a) lies on line`(y)/(2) = 3 - 6`.Find the value of a.
With out Pythagoras theorem, show that A(4, 4), B(3, 5) and C(-1, -1) are the vertices of a right angled.
Find the image of a point (-1, 2) in the line joining (2, 1) and (- 3, 2).
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.
Determine whether the following points are collinear. A(–1, –1), B(0, 1), C(1, 3)
Given: Points A(–1, –1), B(0, 1) and C(1, 3)
Slope of line AB = `(square - square)/(square - square) = square/square` = 2
Slope of line BC = `(square - square)/(square - square) = square/square` = 2
Slope of line AB = Slope of line BC and B is the common point.
∴ Points A, B and C are collinear.
Four alternative answers for the following question are given. Choose the correct alternative and write its alphabet:
Slope of X-axis is ______.
