Find the ratio in which the point (x, -1) divides the line segment joining the points (-3, 5) and (2, -5). Also find the value of x

Let the point P (x, - 1) divides the line segment joining the points A (-3, 5) and B (2, -5) in the ratio k : 1. Then

fraction numerator k m space x space left parenthesis negative 5 right parenthesis space plus space 1 space x space 5 over denominator k space plus space 1 end fraction equals space minus 1 rightwards double arrow space space fraction numerator negative 5 k space plus space 5 over denominator k space plus 1 end fraction equals negative 1 rightwards double arrow space minus 5 k space plus space 5 space equals space minus k space minus 1 rightwards double arrow space space space minus 4 k space equals space minus 6 rightwards double arrow space space space space space space k equals 6 over 4 equals 3 over 2

Hence, the required ratios is 3 : 2.

Also space space space space space space space space straight x space equals space fraction numerator 3 cross times 2 plus 2 cross times left parenthesis negative 3 right parenthesis over denominator 3 plus 2 end fraction equals fraction numerator 6 minus 6 over denominator 5 end fraction equals 0

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Coordinate Geometry

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