Segment Division

Question

Find the coordinates of the points which divides the line segment joining the points (x+y,x-y) and (x-y,x+y) internally in the ratio x:y

Answer 1

Let point is (x0, y0). Then: (x₀ - x - y)/(x - y - x₀) = x/y and (y₀ - x + y)/(x + y - y₀) = x/y;

yx₀ - xy - y² = x² - xy - xx₀; x₀ = (x² + y²)/(x + y);

yy₀ - xy + y² = x² + xy - xy₀; y₀ = (x² - y² + 2xy)/(x + y)