Straight line
How do you find the equation of an altitude
1) calculate the gradient of the side which is perpendicular to the altitude 2) calculate the gradient of the altitude using m x m⊥ = -1 3) find the equation using this gradient and the point that the altitude passes through In short- m⊥A, mA, e
How do you find the equation of the perpendicular bisector
1) calculate the midpoint of the line segment being bisected 2) calculate the gradient of the line used in step 1, then find the gradient of its perpendicular bisector using m x m⊥ = -1 3) find the equation of the perpendicular bisector using the point from step 1 and the gradient from step 2.
How do you find the equation of a median
1) calculate the midpoint of the relevant (opposite) line 2) calculate the gradient of the line between the midpoint and the opposite vertex 3) find the equation using this ^ gradient and either of the two points used in step 2. In short- M, m, e.
How to test if the points A, B and C are collinear
1) work out mAB 2) work out mBC (or mAC) 3) if the gradients from 1&2 are the same then A, B and C are collinear.
What is a median of a triangle
A line through a vertex and the midpoint of the opposite side
What is an altitude of a triangle
A line through a vertex perpendicular to the opposite side
What is a perpendicular bisector
A line which cuts through the midpoint of a line segment at right angles
What is the rule for finding the gradient of a perpendicular line
If you know the gradient of one of the lines, then the gradient of the other is calculated by inverting the gradient (flipping the fraction) and changing the sign. Eg) if m=2/3 then m⊥= -3/2
Midpoint formula
M = (x1+x2 ÷2) , (y1+y2 ÷2)
How do you find a point of intersection
Set eqns equal to each other and solve
If m x m⊥ = -1 then...
The lines are perpendicular (⊥)
Distance formula
d = √(x2-x1)²(y2-y1)²
If perpendicular lines have gradients m and m⊥ then....
m x m⊥ = -1
Gradient formula
m= y2-y1/x2-x1 OR m=tanθ
What form must a straight line equation be in before you extract the gradient
y=mx+c
The equation of a straight line
•y-b=m(x-a) •y=mx+c
