Answer to Question #242555 in Geometry for Timmy

Question

Find the coordinate of the point which divides the line joining p(2,1) and Q(3,5), externally in the ratio p:Q

Answer 1

If point C(x3,y3) divides the line PQ, where P(x1,y1), Q(x2,y2) externally in the ratio p:q, it means, that:

$x3=(px2-qx1)/(p-q)$

$y3=(py2-qy1)/(p-q)$

In the case where P(2,1) and Q(3,5) we have:

$x3=(3p-2q)/(p-q)$

$y3=(5p-q)/(p-q)$

So, the coordinate of the point C is ((3p-2q)/(p-q),(5p-q)/(p-q)).