Answer to Question #221070 in Analytic Geometry for ufzz

Question

Find the midpoint and distance of the line segment that connects the following points a) (0,3) and (4,7) b) (-9,6) and (-1, -2) c) (-4.5, -12.5) and (4.5, 13)

Answer 1

The mid point of line segment joining two points ( x₁, y₁ ) and ( x₂, y₂ ) is given by

$(x, y) = \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}$

and the distance between two points is given by

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

a) (0,3) and (4,7)

mid point $(x, y) = \dfrac{0+4}{2}, \dfrac{3+7}{2}$

mid point $(x, y) = (2,\ 5)$

$d = \sqrt{(4-0)^2+(7-3)^2}$

$d = 4\sqrt{2} \ units$

b) (-9,6) and (-1, -2)

mid point $(x, y) = \dfrac{-9-1}{2}, \dfrac{6-2}{2}$

mid point $(x, y) = (-5,\ 2)$

$d = \sqrt{(-1+9)^2+(-2-6)^2}$

$d = 8\sqrt{2} \ units$

c) (-4.5, -12.5) and (4.5, 13)

mid point $(x, y) = \dfrac{-4.5+4.5}{2}, \dfrac{-12.5+13}{2}$

mid point $(x, y) = (0,\ 0.25)$

$d = \sqrt{(4.5+4.5)^2+(13+12.5)^2}$

$d = 27.04 \ units$