Advertisements
Advertisements
प्रश्न
Verify whether the following points are collinear or not:
A(1, –3), B(2, –5), C(–4, 7).
उत्तर
A ≡ (1, –3) ≡ (x1 ,y1),
B ≡ (2, –5) ≡ (x2, y2),
C ≡ (–4, 7) ≡ (x3, y3).
Slope of AB = ` (y_2 - y_1)/(x_2 - x_2)`
`=(-5 - (-3))/(2 - 1)`
`= (-5 + 3)/(2 - 1)`
= `(-2)/1`
= –2
Slope of BC = `(y_3 - y_2)/(x_3 - x_2)`
`= (7 - (-5))/(-4 - 2)`
= `(7 + 5)/(-4-2)`
`= 12/-6`
= –2
A, B, and C are collinear points that have B as a common point.
APPEARS IN
संबंधित प्रश्न
A and B are two points on the x-axis and y-axis respectively. P (2, −3) is the midpoint of AB. Find the:
(1) coordinates of A and B
(2) slope of line AB.
(3) an equation of line AB.
Find the slope of the line perpendicular to AB if : A = (0, −5) and B = (−2, 4)
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 of the line which is parallel to x + 2y + 3 = 0
Lines mx + 3y + 7 = 0 and 5x – ny – 3 = 0 are perpendicular to each other. Find the relation connecting m and n.
If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.
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.
E(–4, –2) , F (6, 3)
Determine whether the following point is collinear.
R(1, –4), S(–2, 2), T(–3, 4)
Find k, if PQ || RS and P(2, 4), Q (3, 6), R(3, 1), S(5, k).
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 type of the quadrilateral if points A(–4, –2), B(–3, –7) C(3, –2) and D(2, 3) are joined serially.
Find the slope of a line, correct of two decimals, whose inclination is 30°
Find the slope of a line passing through the given pair of points (0,5) and (5,0)
Find the slope of a line parallel to the given line 4x-2y = 3
Find the slope and the y-intercept of the following line 4y = 5x - 8
Find the slope and the y-intercept of the following line 2x + 3y = 12
Show that the line joining (2, – 3) and (- 5, 1) is:
(i) Parallel to line joining (7, -1) and (0, 3).
(ii) Perpendicular to the line joining (4, 5) and (0, -2).
Find the image of a point (-1, 2) in the line joining (2, 1) and (- 3, 2).
