Question

Show that the co-ordinates of the point which divides the line segment joining the points \( (a+b, a-b) \) and \( (a-b, a+b) \) in the ratio \( 3: 2 \) is  (\(\frac{5a-b}5\), \(\frac{5a+b}5\))

Answer 1

Let point p(x, y) divides the line segment joining the points A(a + b, a - b) & B(a - b, a + b) in the ratio 3 :2

\(\therefore\) By section formula,

x = \(\frac{3(a-b)+2(a+b)}{3+2}\) = \(\frac{3a-3b+2a+2b}{5}\) = \(\frac{5a-b}5\)

y = \(\frac{3(a+b)+2(a-b)}{3+2}\) = \(\frac{3a+3b+2a-2b}5 = \frac{5a+b}5\) 

Required points is P(\(\frac{5a-b}5\), \(\frac{5a+b}5\)) which divides line segment joining points (a + b, a - b) and (a - b, a + b) in the ratio 3 : 2