Question

Into how many parts do 50 concurrent lines divide the plane?

Answer 1

50 concurrent lines divide the plane in 100 parts.

Explanation:

Table given in the picture attached,

Number of lines 1 2 3 4 5 n 50

Parts of plane 2 4 6 8 10 2n 100

There is a proportional relationship between the number of lines (x) and parts of plane (y).

y ∝ x

y = kx

For x = 1 and y = 2,

2 = 1(k)

k = 2

Therefore, equation will be,

y = 2x

For 50 concurrent lines, number of planes will be,

y = 2 × 50

= 100 planes