Question

Find the co-ordinates of the mid-point of the line segment joining the following points:

(−2, −4) and (−3, 2)

Answer 1

Midpoint formula:

Midpoint of (x₁, y₁) and (x₂, y₂) is,

M = `((x_1 + x_2) / 2), ((y_1 + y_2) / 2)`

Substituting the given points:

x₁ = −2, y₁ = −4;

x₂ = −3, y₂ = 2

Compute the x-coordinate:

`(x_1 + x_2) / 2 = (−2 + (−3)) / 2`

= `(−5) / 2`

= `−5 / 2`

∴ x-coordinate = −2.5

Compute the y-coordinate:

`(y_1 + y_2) / 2 = (−4 + 2) / 2`

= `(−2) / 2`

∴ y-coordinate = −1

Hence, the co-ordinates of the mid-point of the line segment joining the points are (`−5 / 2`, −1)