Question

The distance of(0,2) from the midpoint of the line segment joining (4,10) and (2,2) is

Answer 1

Formula used:

1. The midpoint of line segment joining

$({x_1},{y_1}) and ({x_2},{y_2})$ is

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

2. Distance formula

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

The midpoint of the line segment joining (4,10)and(2,2) is

$(\frac{4+2}{2},\frac{10+2}{2})$

(3,6)

Now, the distance between (0,2)and(3,6) is

$d=\sqrt{ {(0-3)}^2+{(2-6)}^2}}\\d=\sqrt{(-3)^2+(-4)^2}\\d=\sqrt{9+16}\\d=\sqrt{25}$

d=5

Answer 2

First of all we need to calculate the midpoint of line joining points  (4,10) and (2,2)

Mid point of a line shall be (x1+x2)/2 and y1+y2)/2

i.e. (4+2)/2 = 3 and (10+2)/2= 6

Midpoint is (3,6)

Now the distance between points is calculated by formula  

D= square root of {(x1-x2)^2+(y1-y2)^2}

=  Square root of {(0-3)^2+(2-6)^2}

= Square root of (9+16)

= Square root of 25

= 5

Distance between the point (0,2) and (3,6) is 5 units