Cambridge International Mathematics

308 Straight lines (Chapter 14)

EXERCISE 14E

1 Draw the graph of the line with equation:

a y=2x+3 b y=^12 x¡ 3 c y=¡x+5

d y=¡ 4 x¡ 2 e y=¡^13 x f y=¡ 3 x+4

g y=^34 x h y=^13 x¡ 1 i y=¡^32 x+2

2aThe line with equationy=2x¡ 1 is reflected in thex-axis. Graph the line and draw its image.

Find the equation of the reflected line.

b The line with equation y=^12 x+2is reflected in they-axis. Graph the line and draw its image.

Find the equation of the reflected line.

3 Use axes intercepts to draw sketch graphs of:

a 2 x+y=4 b 3 x+y=6 c 3 x¡ 2 y=12

d 3 x+4y=12 e x¡y=2 f x+y=¡ 2

g 2 x¡ 3 y=¡ 9 h 4 x+5y=20 i 5 x¡ 2 y=¡ 10

4aGraph the line with equation 3 x+2y=1and show that(¡ 1 ,2)lies on it.

b If the line with equation 3 x+2y=1is rotated clockwise about the point(¡ 1 ,2)through an

angle of 90 o, find the equation of the rotated line.

5 Graph the line with equation 3 x¡ 5 y=15. If the line is rotated anticlockwise about the origin through

an angle of 180 o, find the equation of this new line.

Many geometrical shapes havelines of symmetry. If the shape is drawn on the Cartesian plane, we can use

the information learnt in this chapter to find the equations of the lines of symmetry.

Example 9 Self Tutor

Consider the points A(1,3),B(6,3) and C(6,1).

a Plot the points and locate D such that ABCD is a rectangle.

b State the coordinates of D.

c Write down the equations of any lines of symmetry.

abDisat(1,1)

c l 1 is a vertical line withx-coordinate midway between

1 and 6.

) its equation is x=1+6 2 =3: 5

l 2 is a horizontal line with y-coordinate midway

between 1 and 3.

) its equation is y=3+1 2 =2.

So, the lines of symmetry have equations x=3: 5

and y=2.

F LINES OF SYMMETRY [7.8]

O

AB

DC

16

1

3

x

y lz

lx

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Y:\HAESE\IGCSE01\IG01_14\308IGCSE01_14.CDR Monday, 13 October 2008 10:43:41 AM PETER