Cambridge Additional Mathematics

Straight line graphs (Chapter 7) 183

EXERCISE 7A.2

1 Consider the points P(¡ 3 ,7) and Q(1,¡5). Find:

a the distance between P and Q

b the midpoint of PQ

c the gradient of PQ

d the equation of the perpendicular bisector of PQ.

2 Find the equation of the perpendicular bisector of AB given:

a A(3,¡3) and B(1,¡1) b A(1,3) and B(¡ 3 ,5)

c A(3,1) and B(¡ 3 ,6) d A(4,¡2) and B(4,4).

3 Consider the points P(¡ 1 ,5) and Q(3,7). The perpendicular bisector of PQ cuts thex-axis at R.

Find the area of triangle PQR.

To find where straight lines meet, we need to solve the equations of the lines simultaneously.

Example 8 Self Tutor

Find where the line:

a y=2x¡ 5 meets the line 4 x+3y=15

b x+3y=5meets the line 2 x¡ 5 y=¡ 12.

a Substituting y=2x¡ 5 into 4 x+3y=15 gives

4 x+ 3(2x¡5) = 15

) 4 x+6x¡15 = 15

) 10 x=30

) x=3 and y= 2(3)¡5=1

The lines meet at (3,1).

b x+3y=5,sox=5¡ 3 y.

Substituting x=5¡ 3 y into 2 x¡ 5 y=¡ 12 gives

2(5¡ 3 y)¡ 5 y=¡ 12

) 10 ¡ 6 y¡ 5 y=¡ 12

) ¡ 11 y=¡ 22

) y=2 and x=5¡3(2) =¡ 1

The lines meet at (¡ 1 ,2).

EXERCISE 7B

1 Find the intersection point of each pair of lines:

a y=4x¡ 1 and 2 x+y=5 b y=9¡ 2 x and 4 x+3y=15

c x+4y=7and 5 x¡ 2 y=¡ 31 d 3 x+y=¡ 5 and 4 x¡ 7 y=10.

B Intersection of straight lines

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Y:\HAESE\CAM4037\CamAdd_07\183CamAdd_07.cdr Friday, 20 December 2013 3:23:56 PM BRIAN