Cambridge International Mathematics

Straight lines (Chapter 14) 311

5 Find the equation of a line with gradient^23 which passes through (¡ 3 ,4).

6 Use axes intercepts to draw a sketch graph of 3 x¡ 2 y=6.

7 Findkif (¡ 3 ,¡1) lies on the line 4 x¡y=k.

8 Find the equation of a line with zero gradient that passes through (5,¡4).

9 Find, in general form, the equation of a line parallel to 2 x¡ 3 y=10 which passes through

(3,¡4).

10 Draw the graph of the line with equation y=^34 x¡ 2.

11 Given A(¡ 3 ,1),B(1,4)and C(4,0):

a Show that triangle ABC is isosceles.

b Find the midpoint X of line segment AC.

c Use gradients to verify that line segments BX and AC are perpendicular.

d Find the equations of any lines of symmetry of triangle ABC.

12 Consider the points A(3,¡2),B(8,0),C(6,5) and D(1,3).

a Prove that line segments AB and DC are parallel and equal in length.

b Prove that line segments AB and BC

c Classify the quadrilateral ABCD.

d

Review set 14B

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1aFind the equation of thex-axis.

b Write down the gradient andy-intercept of a line with equation y=5¡ 2 x.

c Find, in general form, the equation of a line with gradient¡^47 which passes through (¡ 2 ,2).

2 Determine the equation of the illustrated line:

3 Find, in gradient-intercept form, the equation of a line:

a with gradient¡ 2 andy-intercept 7

b passing through(¡ 1 ,3) and (2,1)

c parallel to a line with gradient^32 and passing through(5,0).

4 If (k,5) lies on a line with equation 3 x¡y=¡ 8 , findk.

x

y

-1

2

O

Find the equations of all lines of symmetry of ABCD.

are perpendicular and equal in length.

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Y:\HAESE\IGCSE01\IG01_14\311IGCSE01_14.CDR Monday, 10 November 2008 9:08:46 AM PETER