Answer to Question #242555 in Geometry for Timmy

Question #242555
Find the coordinate of the point which divides the line joining p(2,1) and Q(3,5), externally in the ratio p:Q
1
Expert's answer
2021-09-27T16:40:42-0400


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=(px2qx1)/(pq)x3=(px2-qx1)/(p-q)

y3=(py2qy1)/(pq)y3=(py2-qy1)/(p-q)

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

x3=(3p2q)/(pq)x3=(3p-2q)/(p-q)

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

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


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