Question

Find the distance between point (-1, -3) and the midpoint of the line segment joining (2, 4) and (4, 6).

Answer 1

Answer:

$d=4\sqrt{5}$

Step-by-step explanation:

Midpoint Formula: $(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )$

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

Step 1: Find midpoint m

$m=(\frac{2+4}{2} ,\frac{4+6}{2} )$

$m=(\frac{6}{2} ,\frac{10}{2} )$

$m=(3 ,5 )$

Step 2: Find distance d

$d=\sqrt{(3-(-1))^2+(5-(-3))^2}$

$d=\sqrt{(3+1)^2+(5+3)^2}$

$d=\sqrt{(4)^2+(8)^2}$

$d=\sqrt{16+64}$

$d=\sqrt{80}$

$d=4\sqrt{5}$