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 = 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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Distance

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


Distance1

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

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

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

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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