It is being given that the points A(1, 2), B(0, 0) and C(a, b) are collinear.
Which of the following relations between a and b is true ?
(A) a = 2b
(B) 2a = b
(C) a + b = 0
(D) a - b = 0
Answers
Option (B) 2a = b is correct.
Step-by-step explanation:
The given points are A (1, 2), B (0, 0) and C (a, b).
The area of the triangle ΔABC is
| 1 2 1 |
= 1/2 * | 0 0 1 | square units
| a b 1 |
= 1/2 * [ 1 (0 - b) - 2 (0 - a) + 1 (0 - 0) ] square units
[ expanding along the first row ]
= 1/2 * [ - b + 2a ] square units
Since A, B, C are collinear, the area of the triangle ΔABC is zero. Then
1/2 * [ - b + 2a ] = 0
or, - b + 2a = 0
or, 2a = b
Thus the required relation is 2a = b.
Therefore, option (B) is correct.
Related problem:
Verify that the points (1, 5), (2, 3) and (- 2, - 1) are collinear or not. - https://brainly.in/question/14734828
2a = b is the relation between a and b.
Option B is correct.
We use a condition:
If the three points are collinear then, the area of triangle formed by theses points equals zero.
Given,
A(1, 2), B(0, 0) and C(a, b)
Area of triangle = 1/2 [ x1(y2-y3)+x2(y3-y1)+x3(y1-y2) ]
= 1/2 [ 1 (0-b) + 0 (b-2) + a (2-0) ]
= 1/2 [ -b + 2a ]
= -b/2 + a
as, Area of triangle = 0
=> -b/2 + a = 0
a = b/2
2a = b.
Hence the relation between a and b.