Answer

Two arithmetic progressions have the same common difference.

Let, common difference = d

First term of first A.P. = a

First term of second A.P. = a’

Given that difference between their 100^th term is 100

100^th term of first A.P., a₁₀₀ = a + 99d

100^th term of second A.P., a’₁₀₀ = a’ + 99d

Acc. To question,

a₁₀₀ – a’₁₀₀ = 100

a + 99d – a’ – 99d = 100

a – a’ = 100 (i)

1000^th term of first A.P., a₁₀₀₀ = a + 999d

1000^th term of second A.P., a’₁₀₀₀ = a’ + 999d

Acc. To question,

a₁₀₀₀ – a’₁₀₀₀ = a + 999d – a’ – 999d

= a – a’

a₁₀₀₀ – a’₁₀₀₀ = 100 [from (i)]

Hence, difference between 1000^th term of two A.P. is 100.

OR

Let the ordinate of other end is k

Distance =

On squaring both sides, we get

; ;

Therefore, ordinate is 3 or -9.