For more information visit www.caresa.com.au

THE NUMBER PLANE

Q.1. Plot the following pairs of points on separate number planes; one pair to a number plane.

(a) A(2,1); B(6,4)

(b) P(4,6); Q(-4, 0)

(c) M(-2,-4); N(6,2)

(d) W(-4,-3); X(-2,4)

(e) S(5,4); T(8,2)

Draw two lines parallel to the x-axis so that each line passes through one of the points.

Draw two lines parallel to the y-axis so that each line passes through one of the points.

You should now have a rectangle drawn on the number plane.

Join the two points so that the line joining them forms a diagonal of the rectangle.

For each pair of points answer the following questions.

(i) What is the height of the rectangle, i.e. its length along the y-axis?

(ii) What is the width of the rectangle, i.e. its length along the x-axis?

(iii) Use Pythagoras’ theorem to calculate the length of the diagonal.

(iv) Given that the gradient is equal to rise/run, calculate the gradient of the diagonal.

(v) Mark the mid-point of the diagonal on your diagram. Determine its coordinates.

A straight line can be represented by an equation where x & y are each to the power of 1 (not x² or y³ or to any other power than 1)

It can have the general form where it is equated to 0 e.g. ax + by +c = 0

Or it can be written in the intercept form e.g. y = mx + b

When written in the intercept form, m is equal to the gradient and b is equal to the y-intercept i.e. the value of y when x = 0.

The coordinates of any point on the line will satisfy its equation. If the coordinates of the point do not satisfy the equation then the point is not on the line.

Q.2. Draw the following straight lines on the number plane.

(a) y = 2x + 3

(b) y = 4x – 1

(c) 2y = 8x – 2

(d) 2x – y = 5

(e) x = 2y

For each of the above lines

(i) Determine the gradient

(ii) Determine the y-intercept

(iii) Determine which of the following points lie on each line. (0,0), (1,5), (5,5), (2,7), (-2,-9), (4,8), (8,4)