Question

Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.

Answer 1

Mid point formula = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

Let P = (a, 7) = (x₁, y₁)

Q = (6, 5) = (x₂, y₂)

∴ (2, b) = `(("a" + 6)/2, (7 + 5)/2)`

∴ `2 = ("a" + 6)/2` and b = `12/2`

⇒ 4 = a + 6 and b = 6

⇒ a = - 2

∴ a = - 2, b = 6