Find the distance of the point (3,4) from the midpoint of the line joining (8,10) and (4,6)
Accepted Solution
A:
Answer:Distance between point [tex](3,4)[/tex] and midpoint of line joining [tex](8,10)[/tex] and [tex](4,6)[/tex] = [tex]5[/tex] units.Step-by-step explanation:Given:Points:[tex]A(3,4)\\B(8,10)\\C(4,6)[/tex]To find distance from point A to midpoint of BC.Midpoint M of BC:[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\\[/tex][tex]M=(\frac{8+4}{2},\frac{10+6}{2})\\[/tex] [Plugging in points [tex]B(8,10)\ and\ C(4,6)[/tex]][tex]M=(\frac{12}{2},\frac{16}{2})\\[/tex][tex]M=(6,8)\\[/tex]Distance between A and M:[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\[/tex][tex]D=\sqrt{(6-3)^2+(8-4)^2} \\[/tex] [Plugging in points [tex]A(3,4)\ and\ M(6,8)[/tex]][tex]D=\sqrt{(3)^2+(4)^2} \\[/tex][tex]D=\sqrt{9+16} \\[/tex][tex]D=\sqrt{25} \\[/tex][tex]D=\pm5[/tex]Since distance is always positive ∴ [tex]D= 5[/tex] units