Question

If X(3, –2) and Y(–4, 2) are two points and A is a point on XY such that XA : XY = 3 : 5, then the sum of the x-coordinate and y-coordinate of A is

• A. $\frac{-8}{5}$
  
• B. $\frac{4}{5}$
  
• C. $\frac{-4}{5}$
  
• D. $\frac{8}{5}$
  

Answer 1

The correct option is C $\frac{-4}{5}$


Given: $\frac{XA}{XY}=\frac{3}{5}$

$\Rightarrow \frac{XA}{AY}=\frac{3}{2}$


Using the section formula, the coordinates of A are

$=(\frac{3\times (-4)+2\times 3}{3+2},\frac{3\times 2+2\times (-2)}{3+2})$

$=(\frac{-12+6}{5},\frac{6-4}{5})$

$=(\frac{-6}{5},\frac{2}{5})$

∴ Sum of x-coordinate and y-coordinate of A $=\frac{-6}{5}+\frac{2}{5}=\frac{-4}{5}$

Hence, the correct answer is option (c).