# How do you find the midpoint of M(10, –6) and N(–10, –4)?

Mar 6, 2016

color(blue)(P_("mid")" "->( 0,-6))

#### Explanation:

You have two options of approach

Method 1: $\text{ start point "+ 1/2" way}$

Method 2: Mean value

I am opting for mean value

Let first point be$\text{ } {P}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(10 , - 6\right)$
Let second point be$\text{ } {P}_{2} \to \left({x}_{2} , {y}_{2}\right) \to \left(- 10 , - 4\right)$

P_("mid")" "->" "((x_1+x_2)/2,(y_1+y_2)/2)

P_("mid")" "->((10+(-10))/2 ,(-6+(-6))/2)

color(blue)(P_("mid")" "->( 0,-6))

Mar 6, 2016

(0 , -5 )

#### Explanation:

Use the $\textcolor{b l u e}{\text{ mid-point formula }}$

M = [$\frac{1}{2} \left({x}_{1} + {x}_{2}\right) , \frac{1}{2} \left({y}_{1} + {y}_{2}\right)$]

let$\left({x}_{1} , {y}_{1}\right) = \left(10 , - 6\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(- 10 , - 4\right)$

substitute these values into formula.

$\Rightarrow M = \left[\frac{1}{2} \left(10 - 10\right) , \frac{1}{2} \left(- 6 - 4\right)\right] = \left(0 , - 5\right)$