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CBSE Class 10 Answered

Q1. If the point A(2,-4) is equidistant from P(3,8) and Q(-10,y),then find the value of y. Also find distance PQ.
Asked by ravikiran.lagad | 27 Mar, 2018, 01:49: PM
answered-by-expert Expert Answer
begin mathsize 16px style Since comma space point space straight A space is space equidistant space from space points space straight P space and space straight Q. space Therefore comma space AP space equals space AQ space Here space straight A left parenthesis space 2 comma space minus 4 space right parenthesis comma space straight P left parenthesis space 3 comma space 8 space right parenthesis space and space straight Q left parenthesis negative 10 space comma space straight y space right parenthesis. space Since space space AP space equals space AQ Therefore comma bold space bold By bold space bold Distance bold space bold Formula bold space bold colon square root of open parentheses 3 minus 2 close parentheses squared plus open parentheses 8 minus left parenthesis negative 4 right parenthesis close parentheses squared end root space space space equals space square root of open parentheses negative 10 minus 2 close parentheses squared plus open parentheses straight y minus left parenthesis negative 4 right parenthesis close parentheses squared end root therefore comma space square root of open parentheses 1 close parentheses squared plus open parentheses 12 close parentheses squared end root space equals space square root of open parentheses negative 12 close parentheses squared plus open parentheses straight y space plus space 4 close parentheses squared end root therefore comma space space space space space space space space space space space space space space 145 space space space space equals space 144 space plus space straight y squared space plus space 8 straight y space plus space 16 space space space space space space space space space space space space left parenthesis Taking space Square space on space both space the space sides right parenthesis Therefore space space straight y squared space plus 8 straight y space plus space 15 space equals space 0 space comma space by space solving space the space quadratic space equation space we space will space get space the space value space of space straight y. Therefore space space space straight y space equals space minus 5 space space or space space straight y space equals space minus 3 straight P left parenthesis space 3 space comma space 8 space right parenthesis comma space If space straight y space is space minus 5 space the space straight Q left parenthesis negative 10 comma space minus 5 right parenthesis. space space space Therefore space space PQ space equals space square root of open parentheses negative 10 minus 3 close parentheses squared plus open parentheses negative 5 minus 8 close parentheses squared end root equals square root of left parenthesis negative 13 right parenthesis squared space plus space left parenthesis negative 13 right parenthesis squared end root space equals square root of 13 squared space plus space 13 squared end root equals square root of 2 space cross times space 13 squared end root space equals bold space bold 13 square root of bold 2 bold space bold units straight P left parenthesis space 3 space comma space 8 space right parenthesis comma space If space straight y space is space minus 3 space the space straight Q left parenthesis negative 10 comma space minus 3 right parenthesis. space space space Therefore space space PQ space equals space square root of open parentheses negative 10 minus 3 close parentheses squared plus open parentheses negative 3 minus 8 close parentheses squared end root equals square root of 169 plus 121 end root equals square root of bold 290 bold space bold units end style
Answered by Yasmeen Khan | 27 Mar, 2018, 03:17: PM

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