01 Key Concepts
The 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).
Distance Formula
The distance between (x1,y1) and (x2,y2) is sqrt[(x2-x1)^2 + (y2-y1)^2] — derived directly from the Pythagorean theorem.
Midpoint 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.
The Four Quadrants
The plane is divided into four regions by the axes: Quadrant I (+,+), II (-,+), III (-,-), IV (+,-).
Plotting Points
Each point (x,y) is located by moving x units horizontally and y units vertically from the origin.
02 Key Formulas
- Distance = sqrt[(x2-x1)^2 + (y2-y1)^2]
- Midpoint = [(x1+x2)/2, (y1+y2)/2]
03 Solved Examples
Example 1 Find the distance between (0,0) and (3,4).
- Apply the distance formula: sqrt[(3-0)^2 + (4-0)^2] = sqrt[9+16] = sqrt[25].
Answer: 5
Example 2 Find the midpoint of (2,4) and (8,10).
- Average the x-values: (2+8)/2 = 5.
- Average the y-values: (4+10)/2 = 7.
Answer: Midpoint = (5,7)
Example 3 In which quadrant does the point (-3,5) lie?
- x is negative, y is positive.
- This matches Quadrant II.
Answer: Quadrant II
04 Practice Questions
1Find the distance between (0,0) and (6,8).
10
2Find the midpoint of (0,0) and (10,10).
(5,5)
3In which quadrant does (4,-2) lie?
Quadrant IV
4In which quadrant does (-1,-1) lie?
Quadrant III
5Find the midpoint of (1,1) and (5,9).
(3,5)
📄 Coordinate Geometry — Downloadable Worksheet
10 questions with a full answer key. Grab the PDF to print, or try the interactive version in your browser.