Question

The midpoint of the line segment joining (2a, 4) and (-2, 2b) is (1, 2a+1). Find the value of a and b.
show that the points A(- 1, 2), B(2, 5) and C(- 5, – 2) are collinear.

Answer 1

Midpoint of (2a , 4) and (-2 , 2b) is (1 , 2a + 1)
x = `(x_1 + x_2)/(2)`
1 = `(2a - 2)/(2)`
1 = a - 1
∴ a = 2

y = `(y_1 + y_2)/(2)`
2a + 1 = `(4 + 2b)/(2)`
2a + 1 = 2 + b
∴ 5 - 2 = b
∴ b = 3
Therefore, a = 2, b = 3.