Need to Know
The Line
The rules you must have ready for the exam.
How to use this: say each rule in your head, then tap Show me to check.
Plane, midpoint & distance
2 rulesRule 01
Midpoint
Average the coordinates: ((x₁+x₂)/2, (y₁+y₂)/2).
Rule 02
Distance
d = √((x₂-x₁)² + (y₂-y₁)²).
Slope & lines
3 rulesRule 03
Slope
m = (y₂-y₁)/(x₂-x₁). From ax+by+c=0, m = -a/b.
Rule 04
Parallel & perpendicular
Parallel → equal slopes. Perpendicular → slopes multiply to -1.
Rule 05
Equation of a line
y - y₁ = m(x - x₁). For two points, find the slope first.
Drawing
1 ruleRule 06
Intercepts
x=0 gives the y-intercept, y=0 gives the x-intercept; plot both and join.
Area, intersection & the circle
3 rulesRule 07
Area of a triangle
½ |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.
Rule 08
Intersection
The point where two lines cross — solve their equations simultaneously.
Rule 09
The circle
Centre origin: x²+y²=r². Centre (h,k): (x-h)²+(y-k)²=r².
Mathslive.ie · The Line · Need to Know