Everything Maths Grade 10

40.The following diagram shows△P QRwithP(1; 1). The equation ofQRisx 3 y = 6 and the
equation ofP Risxy2 = 0.RP Q^ =.

2 4 6

 2

2

4

Q

R

P(1;1)

x

y



a)Write down the coordinates ofQ.

b)Prove thatP Q?QR.

c)Write down the gradient ofP R.

d)If they-coordinate ofRis 4, calculate thex-coordinate.

e)Find the equation of the line fromPtoS(the mid-point ofQR).

41.The pointsE(3; 0),L(3; 5)andS(t+ 1;2,5)are collinear.

a)Determine the value oft.

b)Determine the values ofaandbif the equation of the line passing throughE,LandSis

x

a

+

y

b

= 1.

42.Given:A(3;4); B(1;7); C(2;5)andD(0;2).

a)Calculate the distanceACand the distanceBD. Leave your answers in surd form.

b)Determine the coordinates ofM, the mid-point ofBD.

c)Prove thatAM?BD.

d)Prove thatA,MandCare collinear.

e)What type of quadrilateral isABCD?

43.M(2;2)is the mid-point ofABwith pointA(3; 1). Determine:

a) the coordinates ofB. b)the gradient ofAM.

c) the equation of the lineAM. d)the perpendicular bisector ofAB.

44.ABCD is a quadrilateral withA(3; 6); B(5; 0); C(4;9); D(4;3).

 10  5 5 10

 10

 5

5

10

A(3; 6)

B(5; 0)

D(4;3)

E

C(4;9)

x

y

Chapter 8. Analytical geometry 325