Question 3 The point on the x – axis which is equidistant from points (−1, 0) and (5, 0) is (A) (0, 2) (B) (2, 0) (C) (3, 0) (D) (0, 3)
Let Given points be A (−1, 0) and B(5, 0)
Since point is x- axis, it’s y- coordinate will be 0
So, let point be C(a, 0)
Since, Point C is equidistant from A and B
∴ AC = BC
√(( 𝑎−(−1)^2+(0−0)^2 ) = √(( 𝑎−5)^2+(0−0)^2 )
√(( 𝑎+1)^2+0^2 ) =√(( 𝑎−5)^2+0^2 )
√(𝑎^2+1^2+2(𝑎)(1)+0) =√(𝑎^2+5^2−2(𝑎)(5)+0)
√(𝒂^𝟐+𝟏^𝟐+𝟐𝒂) =√(𝒂^𝟐+〖𝟐𝟓〗^𝟐−𝟏𝟎𝒂)
Squaring both sides
𝑎^2+1+2𝑎=𝑎^2+25−10𝑎
1+2𝑎=25−10𝑥
2𝑎+10𝑎=25−1
12𝑎=24
𝑎=24/12
𝒂=𝟐
∴ Required point is (2, 0)
So, the correct answer is (B)
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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