# How do you find the axis of symmetry if only given points (1,-3) and (9,-3)?

Jul 10, 2018

$\textcolor{b l u e}{x = 5}$

#### Explanation:

Notice from the given co-ordinates that the $y$ ordinates are the same. If we were to draw a line segment between these to points, the axis of symmetry would be the perpendicular bisector of this line segment. We can therefore find the axis of symmetry by finding the midpoint of the line segment.

The midpoint of a line segment is given by:

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

Hence:

$\left(\frac{9 + 1}{2} , \frac{- 3 - 3}{2}\right) \to \left(5 , - 3\right)$

We can see the the $x$ co-ordinate is $5$,so:

Axis of symmetry is:

$x = 5$