Module 4 · Geometry
Chapter 47: Coordinate Geometry
Geometry
4 topics
What this chapter covers
The 4 topics below make up Coordinate Geometry on the CAT. Click any topic to open its notes, examples and practice test.
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Formula Reference Sheet
This chapter
Points, distance and division
| Distance between two points | d = √[(x₂−x₁)² + (y₂−y₁)²] |
|---|---|
| Midpoint of a segment | M = ((x₁+x₂)/2 , (y₁+y₂)/2) |
| Internal section (ratio m:n) | ((m·x₂+n·x₁)/(m+n) , (m·y₂+n·y₁)/(m+n)) |
| External section (ratio m:n) | ((m·x₂−n·x₁)/(m−n) , (m·y₂−n·y₁)/(m−n)) |
| Centroid of a triangle | ((x₁+x₂+x₃)/3 , (y₁+y₂+y₃)/3) |
Lines, slope and area
| Slope of a line | m = (y₂−y₁)/(x₂−x₁) |
|---|---|
| Slope–intercept form | y = mx + c |
| Two-point form | (y−y₁) = [(y₂−y₁)/(x₂−x₁)](x−x₁) |
| Intercept form | x/a + y/b = 1 |
| Parallel / perpendicular | parallel: m₁ = m₂ ; perpendicular: m₁·m₂ = −1 |
| Area of a triangle | ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| |
CAT reference
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