Question

The midpoint of the line segment AB shown in the diagram is (4, – 3). Write down the coordinates of A and B.

Answer 1

Let the coordinates of A and Bare (x, 0) and (0, y).
so `x = (mx_2 +  nx_1)/(m + n), y = (my_2 + ny_1)/(m + n)`|
m = 2, n = 3
x₁ = 4, x₂ = 4
y₁ = -5, y₂ = 5
∴ x = `(2 xx 4 + 3 xx 4)/(2 + 3) = (8 + 12)/(5) = (20)/(5)` = 4
y = `(2 xx 5 + 3 xx- 5)/(2 + 3)`
= `(10 - 15)/(5)`
= `(-5)/(5)`
= -1
∴ Co-ordinates of P are (4, -1).

Thus, the coordinates of midpoints of
AB = `((x + 2)/2, (y + 0)/2)`
= `(x/2 , y/2)`
According to question, the coordinates of midpoint = (4, -3)
∴ `x/(2)` = 4, x = 8
`y/(2)` = -3, y = -6
∴ The required points are (9, 0) and (0, -6).