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Need to Know
Need to Know

The Line

The co-ordinate geometry rules you must have ready for the exam.

How to use this: read each heading and say the rule in your head first, then tap Show me to check. This layer is for learning the rules, not testing them.

The Cartesian plane

1 rule
Rule 01

Reading a point

A point is an ordered pair (x, y). The origin is (0, 0).

  • x first: left is −, right is +.
  • y second: down is −, up is +.

Midpoint

2 rules
Rule 02

Midpoint formula

Average the ends:

x1 + x22 , y1 + y22

Rule 03

Working backwards

Given the midpoint and one end, repeat the same jump (across and up/down) to land on the other end.

Distance

1 rule
Rule 04

Distance formula

|AB| = √(x2−x1)2 + (y2−y1)2

It is just Pythagoras on the run and the rise.

Slope

2 rules
Rule 05

Slope formula

m = riserun = y2−y1x2−x1

Rule 06

Reading the sign

Up to the right: m > 0. Down to the right: m < 0. Flat line: m = 0. Vertical line: no slope.

Equation of a line

2 rules
Rule 07

The two forms

y = mx + c   and   y − y1 = m(x − x1)

c is the y-intercept.

Rule 08

Parallel & perpendicular

Parallel: m1 = m2. Perpendicular: m1 m2 = −1.

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