Coordinate Geometry
SSC-CGL Exams
1. Overview
Coordinate Geometry is widely tested in SSC CGL for:
Distance between points
Section formula (dividing line segments)
Equation of a line
Slope of a line
Focus on formulas + diagram visualization for fast solving.
2. Distance Formula
For points A(x₁, y₁) and B(x₂, y₂):
Distance AB = √[(x₂ - x₁)² + (y₂ - y₁)²]
Example 1
A(2,3), B(5,7) → Distance?
AB = √[(5-2)² + (7-3)²] = √[3² + 4²] = √[9 + 16] = √25 = 5
5 units
3. Section Formula
Dividing a line segment AB in ratio m:n:
Internally
P(x, y) = ( (mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n) )
Externally
P(x, y) = ( (mx₂ - nx₁)/(m-n), (my₂ - ny₁)/(m-n) )
Example 2
A(2,3), B(8,7), divide AB in 1:2 internally → P?
x = (1×8 + 2×2)/(1+2) = (8+4)/3 = 4
y = (1×7 + 2×3)/(1+2) = (7+6)/3 = 13/3 ≈ 4.33
P(4, 4.33)
4. Slope of a Line
Slope (m) measures steepness:
m = (y₂ - y₁)/(x₂ - x₁)
m > 0 → line rising
m < 0 → line falling
m = 0 → horizontal
Undefined → vertical
Example 3
A(2,3), B(5,7) → Slope?
m = (7-3)/(5-2) = 4/3
4/3
5. Equation of a Line
Forms
Slope-Intercept Form:
y = mx + c
m = slope, c = y-intercept
Point-Slope Form:
y - y₁ = m(x - x₁)
Two-Point Form:
y - y₁ = [(y₂ - y₁)/(x₂ - x₁)](x - x₁)
Example 4
Find equation of line through A(2,3) and B(5,7)
m = (7-3)/(5-2) = 4/3
Point-slope: y - 3 = 4/3 (x - 2)
Simplify → y = 4/3 x + 1/3
y = 4/3 x + 1/3
6. SSC Short Tricks / Tips
Distance formula → memorize √[(x₂−x₁)²+(y₂−y₁)²]
Section formula → carefully check internal vs external division
Slope → remember: vertical → undefined, horizontal → 0
Equation → if slope m and point (x₁,y₁) → use point-slope form
Quick check: for two points (x₁,y₁), (x₂,y₂) → line equation: (y - y₁)(x₂ - x₁) = (x - x₁)(y₂ - y₁)
Collinearity check: Three points A, B, C → slope AB = slope BC
7. Practice Section
Q1. Distance between P(1,2) and Q(4,6)?
View Answer
√[(4−1)² + (6−2)²] = √(9+16) = √25 = 5
5 units
Q2. Midpoint of A(2,3) and B(8,7)?
View Answer
x = (2+8)/2 = 5, y = (3+7)/2 = 5
M(5,5)
Q3. Slope of line joining A(1,2), B(3,6)?
View Answer
m = (6−2)/(3−1) = 4/2 = 2
2
Q4. Line passing through (2,3) slope = 3 → equation?
View Answer
y−3 = 3(x−2) → y = 3x−6+3 → y = 3x−3
y = 3x−3
Q5. Divide AB(2,4) to (8,10) externally in 2:1 → P?
View Answer
x = (2×8 − 1×2)/(2−1) = (16−2)/1 = 14
y = (2×10 − 1×4)/1 = (20−4) = 16
P(14,16)
Q6. Check collinearity: A(1,2), B(2,4), C(3,6)?
View Answer
Slope AB = (4−2)/(2−1) = 2
Slope BC = (6−4)/(3−2) = 2
Equal → Collinear
Collinear
8. Quick Recap Table
| Topic | Formula / Property | SSC Tip |
|---|---|---|
| Distance | √[(x₂−x₁)²+(y₂−y₁)²] | Check units |
| Midpoint | ((x₁+x₂)/2, (y₁+y₂)/2) | Internal division 1:1 |
| Section | (mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n) | Internal vs external |
| Slope | (y₂−y₁)/(x₂−x₁) | Vertical → undefined, Horizontal → 0 |
| Line Equation | y−y₁ = m(x−x₁) | Point-slope or two-point form |
| Collinearity | Slopes equal | Quick SSC check |
You've completed Article 13: Coordinate Geometry!
Courage Tip: Always draw axes and mark points — most SSC problems can be solved in seconds if the diagram is correct.
Start Your SSC CGL Journey Now!
Join Courage Library to experience disciplined study and expert support.
Be a Couragian!