Everything Maths Grade 10

4.The following picture shows two points on the Cartesian plane,AandB.

 4  3  2  1 1 2

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 2

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1

2

3

4 A(1;y)

B(3;2,5)

x

y

The lineABhas a length of 7,2111. Calculate the missing coordinate of pointB. Round your answer to

one decimal place.

5.Find the length ofABfor each of the following. Leave your answer in surd form.

a) A(2; 7)andB(3; 5) b)A(3; 5)andB(9; 1) c) A(x;y)andB(x+ 4;y1)

6.The length ofCD= 5. Find the missing coordinate if:

a) C(6;2)andD(x; 2). b)C(4;y)andD(1;1).

7.If the distance betweenC(0;3)andF(8;p)is 10 units, find the possible values ofp.

For more exercises, visit http://www.everythingmaths.co.za and click on ’Practise Maths’.

1.2GBT 2.2GBV 3.2GBW 4.2GBX 5a.2GBY 5b.2GBZ

5c.2GC2 6a.2GC3 6b.2GC4 7.2GC5

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8.3 Gradient of a line EMA6B

DEFINITION: Gradient

The gradient of a line is determined by the ratio of vertical change to horizontal change.

Gradient (m) describes the slope or steepness of the line joining two points. In the figure below, lineOQis
the least steep and lineOTis the steepest.

 1 1 2 3 4

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1

2

3

(^4) T S
R
Q
O
x
y
Chapter 8. Analytical geometry 293