Everything Maths Grade 10

 6  5  4  3  2  1 1 2

 3

 2

 1

1

2

3

F(2; 1)

G(6; 3)

H(2;3)

M

x

y

19.In the diagram below, the vertices of the quadrilateral areF(2; 0),G(1; 5),H(3; 7)andI(7; 2).

1 2 3 4 5 6 7

1

2

3

4

5

6

7

H(3; 7)

G(1; 5)

I(7; 2)

F(2; 0)

x

y

a)Calculate the lengths of the sides ofF GHI.

b)Are the opposite sides ofF GHIparallel?

c)Do the diagonals ofF GHIbisect each other?

d)Can you state what type of quadrilateralF GHIis? Give reasons for your answer.

20.Consider a quadrilateralABCDwith verticesA(3; 2),B(4; 5),C(1; 7)andD(1; 3).

a)Draw the quadrilateral.

b)Find the lengths of the sides of the quadrilateral.

21.ABCDis a quadrilateral with verticesA(0; 3),B(4; 3),C(5;1)andD(1;1).

a)Show by calculation that:

i. AD=BC ii.AB∥DC

b)What type of quadrilateral isABCD?

c)Show that the diagonalsACandBDdo not bisect each other.

22.P,Q,RandSare the points(2; 0),(2; 3),(5; 3)and(3;3)respectively.

a)Show that:

i. SR= 2P Q ii.SR∥P Q

b)Calculate:

i. P S ii.QR

c)What kind of quadrilateral isP QRS? Give reasons for your answer.

Chapter 8. Analytical geometry 321