# Exercise: Coordinate and Graphs

## Distance in the Coordinate Plane

**The Distance Formula:**The distance between points (x

_{1,}y

_{1}) and (x

_{2},y

_{2}) is given by the formula Note: This is really the Pythagorean Theorem in a different form.

- Plot the points (0,0) and (-4,3).
- Measure the distance between the two points.

What distance did you get above? Find the distance manually (by calculating) to check your answer from Geogebra.

## Midpoints in the Coordinate Plane

To find the midpoint of a segment on a coordinate plane, find the average of your x and an average of your y values.

- Plot the points (-1,-3) and (3, 2).
- Connect the points with a segment and find the midpoint.

What were the coordinates of the midpoint you calculated above?

## Graph an equation

- Draw a graph that has symmetry with respect to the x-axis by inputting the equation in the (+) sign.
- Draw another graph that has symmetry with respect to the y-axis by inputting the equation in the (+) sign. You should use different name so that both graphs appear (for example: f(x) for no.1 and g(x) for no. 2).

## Symmetry

Explain three ways to check for symmetry