Straight lines/Triangles

Question 1

How would you define & prove COLLINEARITY?

Answer 1

If 3 or more points lie on a straight line they are collinear.
For example: Points A, B & C are collinear if…
mab = mbc & lines AB and BC have a common point

Question 2

What statement should you use when proving 3 points are collinear?

Answer 2

Since mab = mbc and there is a common point B, points A, B & C are collinear

Question 3

Two lines are parallel if…

Answer 3

They have equal gradients/ m1 = m2

Question 4

How would you find perpendicular gradients?

Answer 4

m1 x m2 = -1

Question 5

What is a median of a triangle?

Answer 5

A line through a vertex and the midpoint of the opposite side

Question 6

What is the method for finding the equation of a median of a triangle?

Answer 6

Find midpoint of side opposite vertex. Calculate gradient between vertex and midpoint. Use gradient and coordinate of vertex in equation of a straight line.

Question 7

What is a perpendicular bisector?

Answer 7

A line which cuts through the midpoint of another line at right angles

Question 8

What is the method for finding the equation of a perpendicular bisector?

Answer 8

Find the midpoint of the line. Calculate the gradient of the line. Calculate the perpendicular gradient. Use the perpendicular gradient and the coordinate of the midpoint in equation of a straight line.

Question 9

What is an altitude of a triangle?

Answer 9

A line through a vertex perpendicular to the opposite side

Question 10

What is the method for finding the equation of an altitude of a triangle?

Answer 10

Calculate the gradient of the line opposite the vertex. Calculate the perpendicular gradient. Use perpendicular gradient and coordinate of vertex in equation of a straight line.

Question 11

Often there will be a part c in triangle questions that will ask you to find the coordinates of the point of intersection of the two lines you have calculated the equations of in parts a and b. How would you do this?

Answer 11

Simultaneous equations using your equations from parts a and b

Question 12

The line l1 makes an angle of 30° with the positive direction of the x-axis.
If given a question such as the one above how would you find the gradient of this line?

Answer 12

m = tanΘ

Question 13

How would you calculate a gradient?

Answer 13

m = y2 - y1/ x2 - x1

Question 14

How would you calculate a midpoint?

Answer 14

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

Question 15

What is the distance formula?

Answer 15

d = √(x2 - x1)² + (y2 - y1)²