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

Question

asked Nov 8, 2020 53.6k views

1 Answer

Gstvg · Answer 1 · 2020-11-12T21:24:27+0000

Answer:

Distance between point
and midpoint of line joining
and
=
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 ∴
units