Understanding Engineering Mathematics

7.3.2 Distance between two points

(i)

√

10 (ii) 2 (iii)

√

2

(iv) 2 (v) 1 (vi)

√

2

7.3.3 Midpoint and gradient of a line

A. (i)

(

1

2

,

1

2

)

(ii) (1,−1) (iii)

(

5

2

,

5

2

)

(iv) (0, 2) (v)

(

5

2

, 1

)

(vi)

(

− 3

2

,

− 3

2

)

B. (i) −^13 (ii) ‘infinite gradient’ – vertical line

(iii) 1 (iv) vertical line (v) 0

(vi) − 1

C. (i)

(

1

5

,

3

5

)

(ii)

(

1 ,

− 4

5

)

(iii)

(

12

5

,

12

5

)

(iv)

(

0 ,

9

5

)

(v)

(

12

5

, 1

)

(vi)

(

− 8

5

,

− 7

5

)

7.3.4 Equation of a straight line

A. (i) x+ 3 y− 2 = 0 (ii) x= 1 (iii) x−y= 0

(iv) x=0(v)y=1(vi)x+y+ 3 = 0

B.(i)^23 ,−^43 (ii) − 2 ,^72 (iii) 1, 1

7.3.5 Parallel and perpendicular lines

(a) (i)x+y= 0 (ii) 2x+y= 0 (iii)x−y= 0
(b) (i)x−y+ 2 = 0 (ii)x− 2 y+ 3 = 0 (iii)x+y= 0

7.3.6 Intersecting lines

(i) and (ii) being parallel, never intersect

(i) and (iii) intersect at (1, 0)

(ii) and (iii) intersect at

( 5

4 ,

1

4

)

7.3.7 Equation of a circle

A. (i) x^2 +y^2 + 2 x− 2 y− 14 = 0 (ii) x^2 +y^2 − 4 x+ 2 y+ 4 = 0

(iii) x^2 +y^2 − 8 x− 2 y+ 13 = 0