Geometry · Quick Reference

Coordinate Geometry Cheat Sheet

Geometry · Lesson 9/16

In one line: coordinate geometry places shapes onto a grid using x and y coordinates, letting us use algebra to measure distances, midpoints, and slopes precisely.

Key Ideas

1The Coordinate Plane. A flat grid formed by a horizontal x-axis and vertical y-axis, meeting at the origin (0,0). Points are located using ordered pairs (x,y).

2Distance Formula. The distance between (x1,y1) and (x2,y2) is sqrt[(x2-x1)^2 + (y2-y1)^2] — derived directly from the Pythagorean theorem.

3Midpoint Formula. The midpoint between (x1,y1) and (x2,y2) is [(x1+x2)/2, (y1+y2)/2] — the average of the x-values and the average of the y-values.

4The Four Quadrants. The plane is divided into four regions by the axes: Quadrant I (+,+), II (-,+), III (-,-), IV (+,-).

5Plotting Points. Each point (x,y) is located by moving x units horizontally and y units vertically from the origin.

Worked Examples

Find the distance between (0,0) and (3,4).

Find the midpoint of (2,4) and (8,10).

Midpoint = (5,7)

In which quadrant does the point (-3,5) lie?

Quadrant II

Formulas

Distance = sqrt[(x2-x1)^2 + (y2-y1)^2]

Midpoint = [(x1+x2)/2, (y1+y2)/2]

Practice Yourself

Find the distance between (0,0) and (6,8).

Find the midpoint of (0,0) and (10,10).

(5,5)

In which quadrant does (4,-2) lie?

Quadrant IV