Advertisements
Advertisements
प्रश्न
If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b
Advertisements
उत्तर
Since the three points are collinear
Area of a ∆ = 0
`1/2[(x_1y_2 + x_2y_3 + x_3y_1) -(x_2y_1 + x_3y_2 + x_1y_3)]` = 0
`1/2[(-3"b" - 5"a" + 36) - (9"a" + 4"b" + 15)]` = 0
– 3b – 5a + 36 – 9a – 4b – 15 = 0
– 7b – 14a + 21 = 0
– b – 2a + 3 = 0 ...(÷ by 7)
2a + b – 3 = 0
Given 2a + b = 3 ...(1)
a + b = 1 ...(2)
(–) (–) (–)
Subtract (1) and (2) ⇒ a = 2
Substitute the value of a = 2 in (2)
⇒ 2 + b = 1
b = 1 – 2
= – 1
The value of a = 2 and b = – 1
APPEARS IN
संबंधित प्रश्न
The perimeter of a triangular field is 240 dm. If two of its sides are 78 dm and 50 dm, find the length of the perpendicular on the side of length 50 dm from the opposite vertex.
The lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 144 cm. Find the area of the triangle and the height corresponding to the longest side.
The perimeter of an isosceles triangle is 42 cm and its baše is (32) times each of the equal sides. Find the length of each side of the triangle, area of the triangle and the height of the triangle.
A hand fan is made by stitching lo equal size triangular strips of two different types of paper as shown in Fig. 12.28. The dimensions of equal strips are 25 cm, 25 cm and 14 cm. Find the area of each type of paper needed to make the hand fan.
Find the areas of the given plot. (All measures are in metres.)
Determine whether the sets of points are collinear?
(a, b + c), (b, c + a) and (c, a + b)
Using Heron’s formula, find the area of a triangle whose sides are 1.8 m, 8 m, 8.2 m
Find the area of an equilateral triangle whose perimeter is 180 cm
The cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of Rs 3 per m2 is Rs 918.
In the following figure, ∆ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of ∆ABC is constructed. Find the height DF of the parallelogram.
