If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.

Given space colon space fraction numerator AP over denominator AB space end fraction space equals space 3 over 7 rightwards double arrow space fraction numerator AP over denominator AP space plus AB end fraction space equals space 3 over 7 rightwards double arrow space 7 space AP space equals space 3 space AP space plus 3 PB rightwards double arrow space 4 space AP space equals space 3 space PB rightwards double arrow space AP over PB space equals space 3 over 4 Therefore comma space straight P space divides space the space line space segment space AB space space internally space in space the space ratio space 3 colon space 4 Let space left parenthesis straight x space comma space straight y space right parenthesis space be space the space coodinates space of space points space straight P. Using space the space section space formula comma space we space get straight x space equals fraction numerator 3 space straight x space 2 space plus 4 space straight x space left parenthesis negative 2 right parenthesis over denominator 3 space plus 4 space end fraction space equals space minus 2 over 7 space straight y space equals fraction numerator 3 space straight x space left parenthesis negative 4 right parenthesis space plus 4 space straight x space left parenthesis negative 2 right parenthesis over denominator 3 space space plus space 4 space end fraction space equals space minus 20 over 7 Hence space comma space the space coordinated space of space point space straight P space are space space open parentheses negative 2 over 7 space comma fraction numerator negative 20 over denominator 7 end fraction close parentheses

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