Question

The mid-point of the line segment joining (2a, 4) and (–2, 2b) is (1, 2a + 1). Find the values of a and b.

Answer 1

Mid-point of (2a, 4) and (−2, 2b) is (1, 2a + 1),

Therefore using mid-point formula, we have:

`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

2 × 2 + 1 – 2 = b

b = 5 – 2 = 3

Therefore, a = 2, b = 3.