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Question

A point P divides the line segment joining the points A (3, -5) and B (-4, 8) such that APPB=k1. If P lies on the line x + y = 0, then find the value of k.


Solution

given the line AB is divided in the ratio K:1

applying section formula
x equals fraction numerator k asterisk times left parenthesis negative 4 right parenthesis plus 1 asterisk times 3 over denominator k plus 1 end fraction equals fraction numerator 3 minus 4 k over denominator k plus 1 end fraction a l s o space y equals fraction numerator k asterisk times 8 plus 1 asterisk times left parenthesis negative 5 right parenthesis over denominator k plus 1 end fraction equals fraction numerator 8 k minus 5 over denominator K plus 1 end fraction sin c e space p left parenthesis x comma y right parenthesis space s a t i s f i e s space t h e space l i n e space x plus y equals 0 p u t t i n g space v a l u e s space o f space x space a n d space y fraction numerator 3 minus 4 k over denominator k plus 1 end fraction plus fraction numerator 8 k minus 5 over denominator K plus 1 end fraction equals 0 fraction numerator 3 minus 5 minus 4 k plus 8 k over denominator k plus 1 end fraction equals 0 minus 2 plus 4 k equals 0 4 k equals 2 k equals 1 half
 

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