Cambridge International Mathematics

Coordinate geometry (Chapter 12) 273

9 Findbgiven that A(¡ 6 ,2),B(b,0)and C(3,¡4)are collinear.

10 Given A(¡ 3 ,1),B(1,4)and C(4,0):

a Show that triangle ABC is isosceles.

b Find the midpoint X of AC.

c Use gradients to verify that BX is perpendicular to AC.

Review set 12B #endboxedheading

1aFind the midpoint of the line segment joining A(¡ 2 ,3)to B(¡ 4 ,3).

b Find the distance from C(¡ 3 ,¡2)to D(0,5).

c Find the gradient of all lines perpendicular to a line with gradient^23.

2 On different sets of axes, show all points with:

a x-coordinates equal to¡ 3 b y-coordinates equal to 5

c positivex-coordinates and negativey-coordinates.

3 K(¡ 3 ,2)and L(3,m)are 9 units apart. Findm.

4 If M(1,¡1)is the midpoint of AB, and A is(¡ 3 ,2), find the coordinates of B.

5 Find the gradient of the line segment joining:

a (5,¡1)and(¡ 2 ,6) b (5,0)and(5,¡2)

6

a What does the value at A indicate?

b Find the gradients of the line segments AB and BC.

What do these gradients indicate?

c If a straight line segment was drawn from A to

C, what would be its gradient? What would this

gradient mean?

7 AB and CD are both diameters of the circle. Find:

a the coordinates of D

b the radius of the circle.

8 Findcif the line joining A(5,3) to B(c,¡2) is perpendicular to the line with gradient 3.

9 A(¡ 1 ,2),B(3,a)and C(¡ 3 ,7)are collinear. Finda.

10 Given A(¡ 3 ,2),B(2,3),C(4,¡1)and D(¡ 1 ,¡2)are the vertices of quadrilateral ABCD:

a Find the gradient of AB and DC.

b Find the gradient of AD and BC.

c What do you deduce from your answers toaandb?

d Find the midpoints of the diagonals of the quadrilateral. What property of parallelograms does

this check?

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0246

hours worked (h)

charge ($)

A

B

C

The graph alongside shows the amount charged by a

plumber according to the time he takes to do a job.

C,()-2 ¡5

B,()5 ¡4

A,()-3 -2 D

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Y:\HAESE\IGCSE01\IG01_12\273IGCSE01_12.CDR Thursday, 25 September 2008 2:15:48 PM PETER