# How do you find the midpoint of (2,-4) and (5,-2)?

Feb 18, 2016

midpoint $\to \left(x , y\right) \to \left(3 , - 3\right)$

#### Explanation:

Suppose ${x}_{1}$ is the starting point and ${x}_{2}$ is the end point for the x axis. Thus the mid point would $\frac{1}{2}$ the difference added to the start point. The same thing for the y-axis.
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Consider the x-axis:

Let $\left\{{x}_{1} , {x}_{2}\right\} \to \left\{2 , 4\right\}$

Difference is $4 - 2 = 2$

half way from ${x}_{1} \to \frac{2}{2} = 1$

So the x-coordinate for $\frac{1}{2}$ way between x_1" and x_2 is:

${x}_{1} + 1 = 2 + 1 = 3$

so ${x}_{\text{midpoint}} = 3$
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In the same way:

${y}_{\text{midpoint}} = {y}_{1} + \frac{{y}_{2} - {y}_{1}}{2} = - 4 + \frac{\left(- 2\right) - \left(- 4\right)}{2}$

y_("midpoint")=" "-4 +(-2+4)/2" " =" " -4 +1 " "=" " -3
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so midpoint $\to \left(x , y\right) \to \left(3 , - 3\right)$