Straight Line

Question 1

What are the gradient formulas

Answer 1

M=y2-y1/x2-x1. m=tanø. Gradient = vertical/horizontal

Question 2

What do parallel lines have in common

Answer 2

Parallel lines have the same gradient

Question 3

Distance formula

Answer 3

D=square root of x2-x1 squared + y2-y1 squared

Question 4

Midpoint formula

Answer 4

M = (x1+x2/2 , y1+y2/2)

Question 5

Collinearity

Answer 5

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

Question 6

Method to prove A,B+C are collinear

Answer 6

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

Question 7

What are perpendicular lines

Answer 7

If two lines with gradients m1 and m2 are perpendicular then m1xm2 =-1

Question 8

To find the perpendicular gradient

Answer 8

1) flip the fraction
2) change the sign

Question 9

To find equation of a median

Answer 9

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)

Question 10

To find the equation of the altitude

Answer 10

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)

Question 11

What is perpendicular bisector?

Answer 11

A perpendicular bisector is a line which cuts through the midpoint of another line at right angles

Question 12

To find the equation of a perpendicular bisector

Answer 12

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)

Question 13

How to show that equations are concurrent

Answer 13

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

Question 14

Intersection of lines

Answer 14

Work out the equation of two lines and use them in simultaneous equations to get a new coordinate

Question 15

When does a line cut the x axis

Answer 15

Cuts the x axis when y=0

Question 16

When does a lone cut the y axis

Answer 16

Cuts y axis when x =0

Question 17

If you are trying to find gradient of a line and the y intercept..

Answer 17

Rearrange to y=mx+c and then state m and c

Question 18

What are the four types of lime for types of gradient

Answer 18

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)

Question 19

How to work out question which asks about positive direction of the x axis

Answer 19

Work out m using gradient formula or from straight line y=mx + c and then sub m inti m=tan0

Question 20

To use m=tan0 what must angle be

Answer 20

Angle must be on the positive side of the line

Question 21

To use m=tan0 what must angle be

Answer 21

Angle must be on the positive side of the line

Question 22

To show a triangle is right angled using perpendicular gradients

Answer 22

The gradient of one and the gradient of the other multiplied will equal -1