Question 41

Point A (2, 1) divides segment BC in the ratio 2:3. Co-ordinates of B are (1, -3) and C are (4, y). What is the value of y?

Solution

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 A (2,1) divides (1,-3) and (4,y) in ratio = 2 : 3

=> $$1 = \frac{(-3 \times 3) + (y \times 2)}{2 + 3}$$

=> $$2y-9 = 5$$

=> $$2y = 5+9=14$$

=> $$y=\frac{14}{2}=7$$

=> Ans - (D)

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