The coordinates of the point which is equidistant from the three vertices of the โ AOB as shown in the Fig. 7.1 is
(A)(x, y)
(B) (y, x)
(C) (x/2,y/2)
(D) (x/2,y/2)
Last updated at Aug. 16, 2021 by Teachoo
Transcript
Question 18 The coordinates of the point which is equidistant from the three vertices of the โ AOB as shown in the Fig. 7.1 is (x, y) (B) (y, x) (C) (๐ฅ/2,๐ฆ/2) (D) (๐ฅ/2,๐ฆ/2) Let Required point = P (p, q) Since point P is equidistant from A, B & C Hence, OP = AP = BP Now, OP = โ(( ๐ โ0)^2+(๐โ0)^2 )= โ(๐^๐+๐^๐ ) Finding AP AP = โ((๐ โ0)^2+(๐โ2๐ฆ)^2 ) = โ(๐^๐+๐^๐+๐๐^๐โ๐๐๐) Finding BP BP = โ((๐ โ2๐ฅ)^2+(๐โ0)^2 ) = โ(๐^๐+๐๐^๐โ๐๐๐+๐^๐ ) Now, OP = AP โ(๐^2+๐^2 ) = โ(๐^2+๐^2+4๐ฆ^2โ4๐๐ฆ) Squaring both sides ๐^2+๐^2 = ๐^2+๐^2+4๐ฆ^2โ4๐๐ฆ 0 = ๐๐^๐โ๐๐๐ 4๐๐ฆ=4๐ฆ^2 ๐=(4๐ฆ^2)/4๐ฆ ๐=๐ Also, OP = BP โ(๐^2+๐^2 ) = โ(๐^2+4๐ฅ^2โ4๐๐ฅ+๐^2 ) Squaring both sides ๐^2+๐^2 = ๐^2+4๐ฅ^2โ4๐๐ฅ+๐^2 0 = ๐๐^๐โ๐๐๐ 4๐๐ฅ=4๐ฅ^2 ๐=(4๐ฅ^2)/4๐ฅ ๐=๐ Thus, Cooridnates of Point P = (p, q) = (x, y) So, the correct answer is (D)
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