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निर्देशांक ज्यामिति

Question
CBSEHHIMAH10010046

बिंदुओं (-3, 10) और (6, -8) को जोड़ने वाले रेखाखंड को बिंदु (-1, 6) किस अनुपात में विभाजित करता है।

Solution

माना बिंदु P(-1, 6), Q(-3, 10) और R(6, -8) को मिलाने वाली रेखा को m:1 में विभाजित करता है।
P के निर्देशांक होंगे
straight P space open square brackets fraction numerator straight m subscript 1 straight x subscript 2 plus straight m subscript 2 straight x subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction comma space fraction numerator straight m subscript 1 straight y subscript 2 plus straight m subscript 2 straight y subscript 1 over denominator straight m subscript 1 plus straight m subscript 2 end fraction close square brackets
यहाँ,
x1 = -3, y1 = 10
x2 = 6, y2 = -8
m1 = m, m2 = 1
इसलिए, P के निर्देशांक होंगे
straight P space open square brackets fraction numerator straight m left parenthesis 6 right parenthesis plus 1 left parenthesis negative 3 right parenthesis over denominator straight m plus 1 end fraction comma space fraction numerator straight m left parenthesis negative 8 right parenthesis plus 1 left parenthesis 10 right parenthesis over denominator straight m plus 1 end fraction close square brackets
equals space straight p space open square brackets fraction numerator 6 straight m minus 3 over denominator straight m plus 1 end fraction comma space fraction numerator negative 8 straight m plus 10 over denominator straight m plus 1 end fraction close square brackets

rightwards double arrow space space minus 1 space equals space fraction numerator straight m space straight x space 6 space plus space 1 space straight x space left parenthesis negative 3 right parenthesis over denominator straight m space plus space 1 end fraction
rightwards double arrow space space minus space straight m space minus space 1 space equals space 6 straight m space minus space 3
rightwards double arrow space space space minus space 1 space plus space 3 space equals space 6 straight m space plus space straight m
rightwards double arrow space space space space space space space space space space space 7 straight m space equals space 2
rightwards double arrow space space space space space space space space space space space space straight m space equals space 2 over 7
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