Coordinate

geometry

12

Contents:

A Plotting points [7.1]

B Distance between two points [7.1, 7.2]

C Midpoint of a line segment [7.3]

D Gradient of a line segment [7.1, 7.4]

E Gradient of parallel and

perpendicular lines [7.5]

F Using coordinate geometry [7.2 - 7.5]

Opening problem

On the given map, Peta’s house is located at point P,

and Russell lives at point R.

a State ordered pairs of numbers which exactly

specify the positions of P and R.

b State the coordinates of the eastern end of the oval.

c Find the shortest distance from Peta’s house to

Russell’s house.

d Locate the point which is midway between Peta’s

house and Russell’s house.

Historical note

History now shows that the two Frenchmen Ren ́e

Descartes and Pierre de Fermat arrived at the

idea of analytical geometryat about the same

time. Descartes’ work “La Geometrie”, however,

was published first, in 1637 , while Fermat’s

“Introduction to Loci” was not published until after

his death.

Today, they are considered the co-founders of

this important branch of mathematics, which links

algebra and geometry

#endboxedheading

René Descartes Pierre de Fermat

y

2 x

4

-4 -2

2

4

-2

-4

city centre

P oval

R

N

O

river

100 m

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Y:\HAESE\IGCSE01\IG01_12\255IGCSE01_12.CDR Thursday, 2 October 2008 12:36:12 PM PETER