Question

Find the midpoint of the segment with the following endpoints.
(10,6) and (4,9)

Answer 1

The coordinates of the midpoint are
`M(x,y) = \left(7, (15)/(2) \right)`, respectively.

Step-by-step explanation:

Given two distinct points (
`A(x,y)`,
`B(x,y)`), the midpoint of the segment (
`M(x,y)`) is determined by the following expression:

`M(x,y) = (1)/(2)\cdot A(x,y) + (1)/(2)\cdot B(x,y)` (1)

If we know that
`A(x,y) = (10, 6)` and
`B(x,y) = (4,9)`, then the coordinates of the midpoint are:

`M(x,y) = (1)/(2)\cdot (10, 6) + (1)/(2)\cdot (4,9)`

`M(x,y) = (5,3) + \left(2,(9)/(2) \right)`

`M(x,y) = \left(7, (15)/(2) \right)`

The coordinates of the midpoint are
`M(x,y) = \left(7, (15)/(2) \right)`, respectively.