Find the point on x-axis which is equidistant from the points (2,–2) and (–4,2)

Find point on x-axis which is equidistant from point (2,-2) and (-4,2)

Question 22 (Choice - 1) - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard - Part 2

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Question 22 (Choice - 1) Find the point on x-axis which is equidistant from the points (2, –2) and (–4, 2) Let the given points be P (2, −2) , Q (−4, 2) Since point equidistant from PQ is on x-axis ∴ It’s y-coordinate will be 0 Let required point be R (x, 0) Now, Point R is equidistant from P & Q Hence, PR = QR √((𝑥 −2)2+(0−(−2))2) = √((𝑥 −(−4))2+(0−2)2) Squaring both sides (√((𝑥 −2)2+(0−(−2))2))^2 = (√((𝑥 −(−4))2+(0−2)^2 ))^2 (𝑥 −2)2+2^2=(𝑥+4)^2+2^2 𝑥^2+2^2−4𝑥+4=𝑥^2+4^2+8𝑥+4 𝑥^2+4−4𝑥+4=𝑥^2+16+8𝑥+4 8−4𝑥=20+8𝑥 8−20=8𝑥+4𝑥 −12=12𝑥 12𝑥=−12 𝑥=(−12)/12 𝒙=−𝟏 ∴ Required point = R (x, 0) = (−1, 0)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.