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ICSE Class 10 Answered

the line segment joining the points (3, -4) and (1,2) is trisected at the points P snd Q. If the ccordinates of P and Q are (p, -2) and (5/3, q) respectively, find the values of p and q    
Asked by sabakkhan21 | 14 Jun, 2018, 11:51: AM
answered-by-expert Expert Answer
begin mathsize 16px style The space line space segment space joining space the space points space straight A left parenthesis space 3 space comma negative 4 right parenthesis space and space straight B left parenthesis 1 comma 2 right parenthesis space is space trisected space at space the space points space straight P space and space straight Q. We space have space straight P left parenthesis straight p comma space minus 2 right parenthesis space and space straight Q left parenthesis 5 over 3 space comma space straight q right parenthesis The space point space straight P space is space the space point space of space trisection space of space the space line space segment space AB. space So comma space straight P space divides space AB thin space in space the space ratio space 1 colon 2. By space section space formula comma straight P space left parenthesis straight p space comma space minus 2 right parenthesis space equals space left parenthesis fraction numerator 2 left parenthesis 3 right parenthesis space plus space 1 left parenthesis 1 right parenthesis over denominator 1 space plus space 2 end fraction comma fraction numerator 2 left parenthesis negative 4 right parenthesis space plus space 1 left parenthesis 2 right parenthesis over denominator 1 space plus space 2 end fraction right parenthesis space equals space left parenthesis 7 over 3 comma space minus 2 right parenthesis rightwards double arrow straight p space equals space 7 over 3 Similarly comma space The space point space straight Q space is space the space point space of space trisection space of space the space line space segment space AB. space So comma space straight Q space divides space AB thin space in space the space ratio space 2 colon 1. straight Q left parenthesis 5 over 3 comma space straight q right parenthesis space equals space left parenthesis fraction numerator 2 left parenthesis 1 right parenthesis space plus space 1 left parenthesis 3 right parenthesis over denominator 1 space plus space 2 end fraction comma fraction numerator 2 left parenthesis 2 right parenthesis space plus space 1 left parenthesis negative 4 right parenthesis over denominator 1 space plus space 2 end fraction right parenthesis space equals space left parenthesis 5 over 2 comma space 0 right parenthesis rightwards double arrow straight q space equals space 0 space space end style
Answered by Yasmeen Khan | 15 Jun, 2018, 10:58: AM

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