Cambridge International Mathematics

310 Straight lines (Chapter 14)

4 Plot the points O( 0 , 0 ), A(1,4),B(9,2) and C(8,¡2).

a Prove that line segments OA and BC are parallel, and OA=BC.

b Prove that line segments OA and AB are perpendicular.

c What have you established about OABC fromaandb?

d Find the midpoints of OA and AB.

e Find the equations of any lines of symmetry of OABC.

5 OABC is a quadrilateral with A(5,0),B(8,4) and C(3,4).

a Plot the points A, B and C and complete the figure OABC.

b Find the equation of line segment BC.

c By finding lengths only, show that OABC is a rhombus.

d Find the midpoints of line segments OB and AC.

e What has been verified ind?

f Find the equations of any lines of symmetry.

6aFind the gradient of line segments AC and BC.

b If ACB is a right angle, useb ato find the value ofk.

c Classify¢ABC.

d State the equation of the line of symmetry of¢ABC.

7 ABC is an equilateral triangle.

a Find the coordinates of C.

b If M and N are the midpoints of line segments BC and

AC respectively, find the coordinates of M and N.

c Find the equations of all lines of symmetry of¢ABC.

Review set 14A #endboxedheading

1aFind the equation of a vertical line through(¡ 1 ,5).

b Determine the gradient of a line with equation 4 x+5y=11.

c Find the axes intercepts and gradient of a line with equation 2 x+3y=6.

d Find, in general form, the equation of a line passing through (¡ 2 ,¡3) and (1,5).

2 Determine the equation of the illustrated line:

3 Find the equation of a line through(1,¡2) and(3,4).

4 Find the equation of a line with gradient¡ 2 andy-intercept 3.

A,()-3 ¡0 O B,()3 ¡0

C,()0 ¡k

y

x

A,()-2 ¡0 O B,()2 ¡0

C

y

x

N M

x

y

8

4

O

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Y:\HAESE\IGCSE01\IG01_14\310IGCSE01_14.CDR Thursday, 2 October 2008 12:30:21 PM PETER