Understanding Engineering Mathematics

B.Plot the points with polar coordinates

(i)

(

3

2

,

3 π

4

)

(ii) (1,π/3) (iii) (1, 120°)(iv)(2,− 60 °)

(v) (2,π/2) (vi) (3,π) (vii)

(

2 ,

5 π

4

)

(viii) (3,− 150 °)

7.3.2 Distance between two points

➤➤

204 208

➤

Find the distance between each pair of points

(i) (−1, 1), (2, 0) (ii) (1, 0), (1,−2)

(iii) (2, 2), (3, 3) (iv) (0, 1), (0, 3)

(v) (2, 1), (3, 1) (vi) (− 2 ,−1), (− 1 ,−2)

7.3.3 Midpoint and gradient of a line

➤➤

204 209

➤

A.Find the midpoint of the line segments joining the pairs of points in RE7.3.2.

B. Ditto for the gradients.

C.Ditto for the points dividing each line segment in the ratio 2 : 3.

7.3.4 Equation of a straight line

➤➤

204 212

➤

A.Find the equations of the straight lines through each pair of points in RE7.3.2.

B. Find the gradients and intercepts of the following lines

(i) 2x− 3 y= 4 (ii) 4x+ 2 y= 7 (iii) x−y+ 1 = 0

C.Show that the equations

y−y 1

x−x 1

=

y 2 −y 1

x 2 −x 1

=m

may be rearranged to give the equation of the straight line as

y−y 1 =

(

y 2 −y 1

x 2 −x 1

)

(x−x 1 )

or

y−y 1 =m(x−x 1 )

Also show that it may be arranged into the ‘symmetric form’

y=

(x−x 1 )

(x 2 −x 1 )

y 2 +

(x−x 2 )

(x 1 −x 2 )

y 1