Question

Find the distance of point (0, 0) from the mid-point of the line segment joining the points (5, −5) and (11, 17).

Answer 1

Midpoint of segment joining (x₁, y₁) and (x₂, y₂):

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

Distance between (x₁, y₁) and (x₂, y₂):

`sqrt[(x_2 − x_1)^2 + (y_2 − y_1)^2]`

Let, find the distance of (0,0) from the midpoint of the segment joining (5, −5) and (11, 17).

Labeling the endpoints:

A = (5, −5), B = (11, 17)

Compute the midpoint M of AB using the midpoint formula:

Mx = `(5 + 11)/2`

Mx = `16/2`

∴ Mx = 8

My = `(−5 + 17)/2`

My = `12/2`

∴ My = 6

So M = (8, 6)

Compute the distance from O = (0, 0) to M = (8, 6) using the distance formula:

OM = `sqrt[(8 − 0)^2 + (6 − 0)^2]`

OM = `sqrt[8^2 + 6^2]`

OM = `sqrt[64 + 36]`

OM = `sqrt[100]`

∴ OM = 10

Hence, the distance is 10 units.