Question

Find the distance of the point (3,4) from the midpoint of the line joining (8,10) and (4,6)

Answer 1

Distance between point
`(3,4)` and midpoint of line joining
`(8,10)` and
`(4,6)` =
`5` units.

Explanation:

Given:

Points:

`A(3,4)\\B(8,10)\\C(4,6)`

To find distance from point A to midpoint of BC.

Midpoint M of BC:

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

`M=((8+4)/(2),(10+6)/(2))\\` [Plugging in points
`B(8,10)\ and\ C(4,6)`]

`M=((12)/(2),(16)/(2))\\`

`M=(6,8)\\`

Distance between A and M:

`D=√((x_2-x_1)^2+(y_2-y_1)^2) \\`

`D=√((6-3)^2+(8-4)^2) \\` [Plugging in points
`A(3,4)\ and\ M(6,8)`]

`D=√((3)^2+(4)^2) \\`

`D=√(9+16) \\`

`D=√(25) \\`

`D=\pm5`

Since distance is always positive ∴
`D= 5` units