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C(-1,4). B(3,3). A(-2,3). D(-1,-3). y. x. Distance. Lengths parallel to the axes are calculated as if it was a number line . Examples 1) Calculate the length of AB. 3 – –2 = 5 u. 2) Calculate the length of CD. 4 – –3 = 7 u. y. ( x 2 , y 2 ). y 2. y 1. ( x 1 , y 1 ).

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Distance

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C(-1,4)

B(3,3)

A(-2,3)

D(-1,-3)

y

x

Distance

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

Examples

1) Calculate the length of AB.

3 – –2 = 5u

2) Calculate the length of CD.

4 – –3 = 7u


y

(x2, y2)

y2

y1

(x1, y1)

(x2, y1)

x

x1

x2

Distance

To calculate the length of a sloping line:

d

(y2y1)

  • Draw a right angled triangle

  • Calculate the horizontal length

(x2x1)

(x2x1)

  • Calculate the vertical length

(y2y1)

  • Use Pythagoras’ theorem

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


Example 1

Calculate the distance between the

points P(6, –1) and Q(–2, 5).

6

8

Does it matter which point is (x1, y1) or (x2, y2)?

NO, either point can be!!!

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


Example 2

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

4

6

I would let the point with negative values be (x1, y1).

If you need an exact answer, make sure you leave it as a surd.

For now we will stop here

BUT, you can simplify

If the question does not specify how it wants the answer, give an exact answer.


Today’s work

SP 9Adv

Exercise 10:01

Pages 334 → 335

Q1→4, a→c

Do some more if you need more practice

Q5 & 6 a, c, e . . .

Yesterday’s work

Exercise 1:11

Q1 & 2a→L,

Q3D,

Q4 & 5 a, c, e…

Exercise 8:01

Q1 & 2 column 1,

Q3 & 4 all


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