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CBSE Class 10 Answered

Two vertex of an isosceles triangle are 2,0 and 2,5 find the third vertex if the length of the equal sides is 3
Asked by anitharajendrakumarchopra | 11 Feb, 2020, 07:41: PM
answered-by-expert Expert Answer
Let A(2, 0), B(2, 5) and C(p, q) be the vertices of triangle ABC where we need to find the coordinates of C
ABC is an isosceles triangle where length of equal sides is 3
L e n g t h space o f space s i d e s space A B equals square root of open parentheses 2 minus 2 close parentheses squared plus open parentheses 0 minus 5 close parentheses squared end root equals 5 T h e r e f o r e comma space t h e space e q u a l space s i d e s space a r e space B C space a n d space A C rightwards double arrow B C equals A C rightwards double arrow square root of open parentheses 2 minus p close parentheses squared plus open parentheses 5 minus q close parentheses squared end root equals square root of open parentheses 2 minus p close parentheses squared plus open parentheses 0 minus q close parentheses squared end root rightwards double arrow open parentheses 2 minus p close parentheses squared plus open parentheses 5 minus q close parentheses squared equals open parentheses 2 minus p close parentheses squared plus q squared rightwards double arrow 25 plus q squared minus 10 q equals q squared rightwards double arrow q equals 5 over 2 A l s o comma space B C equals 3 rightwards double arrow open parentheses 2 minus p close parentheses squared plus open parentheses 0 minus q close parentheses squared equals 9 rightwards double arrow 4 plus p squared minus 4 p plus 25 over 4 equals 9 rightwards double arrow p squared minus 4 p plus 5 over 4 equals 0 rightwards double arrow p equals fraction numerator 4 plus-or-minus square root of 16 minus 4 cross times begin display style 5 over 4 end style end root over denominator 2 end fraction equals fraction numerator 4 plus-or-minus square root of 11 over denominator 2 end fraction H e n c e comma space c o o r d i n a t e s space o f space C thin space a r e space open parentheses fraction numerator 4 plus square root of 11 over denominator 2 end fraction comma 5 over 2 close parentheses space o r space open parentheses fraction numerator 4 minus square root of 11 over denominator 2 end fraction comma 5 over 2 close parentheses
Answered by Renu Varma | 12 Feb, 2020, 10:40: AM

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