Question

In what ratio does the point $P(\frac{10}{3},\frac{-13}{3})$ divide the line segment joining the points A(2, -3) and B(4, -5)?

• A.
  2: 3
• B.
  3:2
• C.
  2:1
• D.
  1:2

Answer 1

The correct option is C

2:1
Let P divide the points A and B in the ratio a:b.

By section formula, we have,

$x=\frac{4a+2b}{a+b}\frac{10}{3}=\frac{4a+2b}{a+b}10(a+b)=3(4a+2b)10a+10b=12a+6b2a-4b=02a=4ba=2b\frac{a}{b}=\frac{2}{1}ORy=\frac{4a+2b}{a+b}-\frac{13}{3}=\frac{-5a-3b}{a+b}-13(a+b)=3(-5a-3b)-13a-13b=-15a-9b2a-4b=02a=4ba=2b\frac{a}{b}=\frac{2}{1}$

Thus, P divides the points A and B in the ratio 2:1.

So, option (c) is correct.