Advertisements
Advertisements
प्रश्न
In each of the following find the value of 'k', for which the points are collinear.
(8, 1), (k, -4), (2, -5)
उत्तर
For collinear points, area of triangle formed by them is zero.
Therefore, for points (8, 1), (k, - 4), and (2, - 5), area = 0
`1/2 [8 { -4- (-5)} + k{(-5)-(1)} + 2{1 -(-4)}] = 0`
8 - 6k + 10 = 0
6k = 18
k = 3
APPEARS IN
संबंधित प्रश्न
If the points A(−2, 1), B(a, b) and C(4, −1) are collinear and a − b = 1, find the values of a and b.
ΔABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm (see the given figure). The height AD from A to BC, is 6 cm. Find the area of ΔABC. What will be the height from C to AB i.e., CE?
The point A divides the join of P (−5, 1) and Q(3, 5) in the ratio k:1. Find the two values of k for which the area of ΔABC where B is (1, 5) and C(7, −2) is equal to 2 units.
prove that the points A (7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right triangle.
Show that the points A (3,1) , B (0,-2) , C(1,1) and D (4,4) are the vertices of parallelogram ABCD.
The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is ______.
Find the value of m if the points (5, 1), (–2, –3) and (8, 2m) are collinear.
Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per m2.
Area of a triangle = `1/2` base × ______.
In the given figure, area of ΔPQR is 20 cm2 and area of ΔPQS is 44 cm2. Find the length RS, if PQ is perpendicular to QS and QR is 5 cm.
