Question

A segment has endpoints (-9,-20) and (14,12). What is the midpoint of this segment?

Answer 1

The midpoint of segment AB is

`\therefore M(x,y)=((5)/(2), -4)`

Explanation:

Given:

Let the end points be

point A( x₁ , y₁) ≡ ( -9 , -20)

point B( x₂ , y₂) ≡ (14 , 12)

M( x , y ) be the Mid point of AB

To Find:

M( x , y ) = ?

Solution:

If M is the midpoint of segment AB then by midpoint formula the M coordinates are given by,

`Mid\ pointM(x,y)=((x_(1)+x_(2) )/(2), (y_(1)+y_(2) )/(2))`

On substituting the values in above formula we get

`M(x,y)=((-9+14 )/(2), (-20+12 )/(2))=((5)/(2), (-8)/(2))`

`\therefore M(x,y)=((5)/(2), -4)`