The point P(5,-2) divides the segment joining the points (x,0) and (0,y) in the ratio 2:5. What is the value of x and y?

Using section formula, the coordinates of point that divides line joining A = $$(x_1 , y_1)$$ and B = $$(x_2 , y_2)$$ in the ratio a : b

= $$(\frac{a x_2 + b x_1}{a + b} , \frac{a y_2 + b y_1}{a + b})$$

Now, point P (5,-2) divides (x,0) and (0,y) in ratio = 2 : 5

=> $$5 = \frac{(2 \times 0) + (5 \times x)}{2 + 5}$$

=> $$x = \frac{5 \times 7}{5} = 7$$

Similarly, $$-2 = \frac{(2 \times y) + (5 \times 0)}{2 + 5}$$

=> $$y = -1 \times 7 = -7$$