Question

find the coordinates of the points which divides line seg QR in the ratio 1:2 where Q (1,1) and R (1,-2)​

Answer 1

Step-by-step explanation:

Let us consider that point P is the point which divides line seg QR in the ratio 1:2.

Suppose the co-ordinates of point P (x,y).

Q(1,1) = x¹ = 1 and y¹ = 1

R(1,-2) = x² = 1 and y² = -2

P(x,y) = x = x and y = y

m = 1 and n = 2

By using section formula

$x \: = \frac{mx {}^{2} + nx {}^{1} }{m + n} \\ \\ x = \frac{1(1) + 2(1)}{1 + 2 } \\ \\ x = \frac{1 + 2}{3} \\ \\ x = \frac{3}{3} \\ \\ x = 1 \\ \\ \\ y = \frac{my {}^{2} + ny {}^{1} }{m + n} \\ \\ y = \frac{1( - 2) + 2(1)}{1 + 2 } \\ \\ y = \frac{ - 2 + 2}{3} \\ \\ y = \frac{0}{3} \\ \\ y = 0$

The co-ordinates of point P is (1,0)