Coordinate geometry

This is a new topic. It is all about lines on a number plane. This is a more in depth study of the straight line we met in the functions topic. We will look at distance, midpoint, gradient, equations of lines, parallel and perpendicular lines, the intersection of lines and perpendicular distance. All but the last portion should have been seen by you in the past.

The HSC has had one whole section of the exam (10%) dedicated to this topic as well as other topics using methods learnt in this topic.

Distance y

x

A BLengths parallel to the axes are calculated as if it was a number line.

Examples1) Calculate the length of AB.

3 – –2 = 5u

2) Calculate the length of CD.

4 – –3 = 7u

C

D

Distance

x

y

(x1, y1)

(x2, y2)

(y2 y1)

(x2 x1) (x2, y1)

x1 x2

y2

y1

To calculate the length of a sloping line:• Draw a right angled triangle

• Calculate the horizontal length

• Calculate the vertical length

• Use Pythagoras’ theorem

If you forget this formula or forget how to apply it, just use Pythagoras’ theorem instead.

Example 1Calculate the distance between the points E(2, 5) and F(–4, 1).

Does it matter which point is (x1, y1) or (x2, y2)?NO, either point can be!!!I would let the point with negative values be (x1, y1).

If you need an exact answer, make sure you simplify any surds.If the question does not specify how it wants the answer, give an exact answer.

Remember to show the units, normally “u” in this style of question

Today’s work

Exercise 7.1Page 272Q 1→3, parts a and cQ 8, 10 & 14