Straight Line Flashcards
What are the gradient formulas
M=y2-y1/x2-x1. m=tanø. Gradient = vertical/horizontal
What do parallel lines have in common
Parallel lines have the same gradient
Distance formula
D=square root of x2-x1 squared + y2-y1 squared
Midpoint formula
M = (x1+x2/2 , y1+y2/2)
Collinearity
For 3 collinear points the gradient between 2 of the points is equal to the gradient between 2 other points and they share a common point
Method to prove A,B+C are collinear
1) calculate the gradient of line AB(mAB)
2) calculate the gradient of line BC(mBC)
3) state since (mAB=mBC) then AB and BC are parallel and since B is a common point A,B and C are collinear
What are perpendicular lines
If two lines with gradients m1 and m2 are perpendicular then m1xm2 =-1
To find the perpendicular gradient
1) flip the fraction
2) change the sign
To find equation of a median
1) calculate the midpoint of the relevant line
2) calculate the gradient between the midpoint and the opposite corner
3) use the gradient and either of the two points used in step 2 in y-b=m(x-a)
To find the equation of the altitude
1) find the gradient of the line which is perpendicular to the altitude (opposite)
2) find the gradient of the altitude (perpendicular gradient m1xm2=-1)
3) use the gradient of the altitude and the point the altitude passes through in y-b=m(x-a)
What is perpendicular bisector?
A perpendicular bisector is a line which cuts through the midpoint of another line at right angles
To find the equation of a perpendicular bisector
1) calculate the midpoint of the line being bisected
2) calculate the gradient of the line used in step 1
3) find the gradient of the perpendicular bisector (perp gradient m1xm2=-1)
4) use the gradient of the perpendicular bisector and the midpoint in y-b=m(x-a)
How to show that equations are concurrent
1) simultaneous equations on 1 and 2
2) if concurrent the answer of simultaneous equations must lie on equation 3
Explanation - since (0,0) lies on the line all three lines are concurrent
Intersection of lines
Work out the equation of two lines and use them in simultaneous equations to get a new coordinate
When does a line cut the x axis
Cuts the x axis when y=0
When does a lone cut the y axis
Cuts y axis when x =0
If you are trying to find gradient of a line and the y intercept..
Rearrange to y=mx+c and then state m and c
What are the four types of lime for types of gradient
Positive gradient - line slopes up From left to right
Negative gradient - line slopes down from left to right
Gradient of zero - line parallel to x axis
Undefined gradient - vertical line (parallel to y axis)
How to work out question which asks about positive direction of the x axis
Work out m using gradient formula or from straight line y=mx + c and then sub m inti m=tan0
To use m=tan0 what must angle be
Angle must be on the positive side of the line
To use m=tan0 what must angle be
Angle must be on the positive side of the line
To show a triangle is right angled using perpendicular gradients
The gradient of one and the gradient of the other multiplied will equal -1
