Everything Maths Grade 10

a)Determine the coordinates ofE, the mid-point ofBD.

b)Prove thatABCDis a parallelogram.

c)Find the equation of diagonalBD.

d)Determine the equation of the perpendicular bisector ofBD.

e)Determine the gradient ofAC.

f)IsABCDa rhombus? Explain why or why not.

g)Find the length ofAB.

45.In the diagram below,f(x) =^32 x 4 is sketched withU(6;a)onf(x).

 10  5 5 10 15 20

 10

 5

5

10

U(6;a)

f(x)

g(x)

x

y

a)Determine the value of a inU(6;a).

b)A line,g(x), passing throughU, is perpendicular tof(x).V(b; 4)lies ong(x). Determine the value

ofb.

c)IfU(6; 5); V(7^12 ;4)andW(1;c)are collinear, determine the value ofc.

46.In the diagram below,MandNare the mid-points ofOAandOBrespectively.

 2 2 4 6 8 10 12

5

10

O

N(5; 2)

M(1; 4)

A

B

x

y

a)Calculate the gradient ofM N.

b)Find the equation of the line throughMandNin the formy=mx+c.

c)Show thatAB∥M N.

326 8.5. Chapter summary