Coordinate Geometry

Question 1

What is the equation of a straight line and what do its values represent?

Answer 1

y = mx + c

Where m is the gradient and c is the y-intercept.

Question 2

When given gradient m and a coordinate (x1, y1) that the line passes through, what equation of a straight line should you use?

Answer 2

y- y1 = m(x- x1)

Question 3

How do you calculate gradient m of a line?

Answer 3

m = y2- y1 ÷ x2- x1

Question 4

How do you calculate the midpoint M of 2 coordinates?

Answer 4

M = (x1 + x2 , y1 +y2) ÷2

Question 5

How do you calculate the distance d (or length) between two coordinates/ points?

Answer 5

d = √(x2- x1)² + (y2- y1)²

Question 6

Define parallel lines

Answer 6

Two lines are parallel if they have the same gradient

Question 7

Define collinear

Answer 7

Coordinates are collinear if they lie on the same straight line

Question 8

Define perpendicular lines

Answer 8

Two lines are perpendicular if m1 x m2 = -1

Question 9

How do you find intersection of two lines and how should you write your answer?

Answer 9

The point of intersection can be found by solving the two equations simultaneously. (Hybrid equation)

Your solutions should be written as a coordinate

Question 10

Define direct proportion

Answer 10

When two quantities both increase or decrease at the same rate.

The graph connecting the quantities will be a straight line

Question 11

What should you say when you are describing limitation of model?

Answer 11

Talk about an assumption mad in the model that would not happen in reality (E.g. air resistance not included)

Question 12

What should you say when you are describing limitation of value?

Answer 12

Talk about something wrong with a value.

E.g. can it be a negative value in reality? Does it make sense in the context?

Question 13

What should you use when you are describing how realistic the model is?

Answer 13

Use the context of the questions to explain how realistic/ not realistic the model is.

Question 14

How do you know the reliability of the model/ estimate?

Answer 14

If the value used to calculate the estimate is inside data range from the question, the estimate is reliable. (Interpolation)

If the value used to calculate the estimate is outside range from the question, the estimate is not reliable.
(Extrapolation)

Question 15

How do you know the suitability of the model?

Answer 15

The calculated value is close to the actual value given, therefore the model suitable.

The calculated value is not close to the actual value given, therefore the model is not suitable

Question 16

How do you know the validity of the model?

Answer 16

A quantity of .. is valid because quantity can be positive / negative.

A quantity .. is not valid because quantity can not be positive / negative.

Question 17

When asked to interpret a value, you need to include:

Context

Value

Units

How do you use these?

Answer 17

Context- Use some of the words from the question

Value- Include the relevant numbers from the question

Units- Write units for all numbers that need them.

Question 18

When interpreting constants in the model ( y intercept and gradient) Wgat should you say for each?

Answer 18

y intercept-
when “x” = 0, “y” = a

Gradient-
the rate of “y” increased by .. as “x” increases by 1 unit

Question 19

What is the Linear Model?

Answer 19

y = a + bx

(Pretty much just y = mx + c but a little different)

Question 20

In the linear model, which constants represent the independent and dependant variables?

Answer 20

y = a + bx

Independent= x

Dependent= y

Question 21

How do you find the perpendicular bisector?

Answer 21

Find perpendicular gradient.

Find midpoint.

Sub into equation of line.

Question 22

How do you find points of intersection?

Answer 22

Solve simultaneous equations/ hybrid equations.