Cambridge Additional Mathematics

182 Straight line graphs (Chapter 7)

b The line cuts thex-axis when y=0

) 3 x¡2(0) =¡ 3

) x=¡ 1

) the line cuts thex-axis at (¡ 1 ,0).

10 Consider the points P(¡ 3 ,¡2) and Q(1,6). A line perpendicular to PQ, passes through Q.

a Find the equation of the line.

b Find the coordinates of the point where the line cuts thex-axis.

11 Suppose A has coordinates (¡ 7 ,4) and B has coordinates (3,¡2). A line parallel to AB, passes

through C(5,¡1).

a Find the equation of the line.

b Find the coordinates of the point where the line cuts they-axis.

12 Suppose P has coordinates (3,8) and Q has coordinates (¡ 5 ,2). The line perpendicular to PQ and

passing through P, cuts thex-axis at R and they-axis at S. Find the area of triangle ORS, where O is

the origin.

PERPENDICULAR BISECTORS

We have already seen that themidpointM of the line segment AB

is the point on the line segment that is halfway between A and B.

The perpendicular bisector of AB is the line which is

perpendicular to AB, and which passes through its midpoint M.

Example 7 Self Tutor

Find the equation of the perpendicular bisector of AB given A(¡ 1 ,2) and B(3,4).

The midpoint M of AB is

³

¡1+3

2

,

2+4

2

́

or M(1,3).

The gradient of AB is

4 ¡ 2

3 ¡(¡1)

=^24 =^12

) the gradient of the perpendicular bisector is ¡^21

fthe negative reciprocal of^12 g

The equation of the perpendicular bisector is y¡3=¡2(x¡1) fusing M(1,3)g

) y¡3=¡ 2 x+2

) y=¡ 2 x+5

M

A,(-1 2)

B,(3 4)

perpendicular

bisector of AB

M

A

B

perpendicular

bisector of AB

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\182CamAdd_07.cdr Monday, 6 January 2014 11:52:51 AM BRIAN