Cambridge Additional Mathematics

184 Straight line graphs (Chapter 7)

2 Linel 1 has equation y=2x+7. Linel 2 passes through (¡ 7 ,6) and (3,0).

a Find the equation ofl 2.

b Find the intersection point ofl 1 andl 2.

3 Find the coordinates of X.

4 In the diagram alongside, a line has been drawn through C,

perpendicular to the line AB. The point of intersection of the

lines is X. Find:

a the equation of AB

b the equation of CX

c the coordinates of X.

Example 9 Self Tutor

ABCD is a trapezium in which AB is parallel to DC,

and ADCb =90±. Find:

a the coordinates of D

b the area of the trapezium.

a Point D is the intersection of AD and DC.

The gradient of AB is

1 ¡ 6

1 ¡(¡4)

=

¡ 5

5

=¡ 1

) DC also has gradient¡ 1 , and has equation y¡(¡6) =¡1(x¡2)

) y+6=¡x+2

) y=¡x¡ 4 .... (1)

AD is perpendicular to DC, so its gradient is 1 , and its equation is y¡6=1(x¡(¡4))

) y¡6=x+4

) y=x+10 .... (2)

Substituting (1) into (2) gives ¡x¡4=x+10

) ¡ 2 x=14

) x=¡ 7 and y=¡(¡7)¡4=3

) Dis(¡ 7 ,3).

A,(-5 8) B,(1 4)

D,(2 0)

C,(-6 -8)

X

A,(-4 6)

B,(1 1)

C,(2 -6)

D

A,(-5 1)

B,(4 4)

C,(0 -4)

X

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_07\184CamAdd_07.cdr Friday, 20 December 2013 3:26:08 PM BRIAN