# How do you find the missing coordinate given one point A(2,8) and the midpoint M(5,4)?

Mar 23, 2017

B(8,0)

#### Explanation:

Subtract the point A x-coordinate from the midpoint x-coordinate (final-initial) to find the distance between them. This will give you 3. Multiply the by 2 because the midpoint is halfway between point A and B. This will give you 6. Add six to point A's x-coordinate and this will give you 8. Do the same process with the y-coordinates to get 0, but be careful of the negative.

Mar 23, 2017

The other point is at $\left(8 , 0\right)$

#### Explanation:

You can substitute the values you have into the midpoint formula:

The midpoint is
"the average of the x-values and the average of the y-values"

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

$\frac{2 + {x}_{2}}{2} = 5 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots} \mathmr{and} \text{ } \frac{8 + {y}_{2}}{2} = 4$

$2 + {x}_{2} = 10 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . .} 8 + {y}_{2} = 8$

${x}_{2} = 8 \textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .} {y}_{2} = 0$

The other point is at $\left(8 , 0\right)$