Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the area of triangle AGF
If (5, 7), (3, p) and (6, 6) are collinear, then the value of p is
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
Find the area of the unshaded region
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm2.
From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
