Question

The point which divides the line segment joining the points(8,-9) and (2,3) in ratio 1:2 internal lies in the
1) first quadrant
2) second quadrant
3) third quadrant
4) fourth quadrant
Please answer quickly

Answer 1

Answer:

(2,3) 1st quadrant

(8,-9)2nd ,,

Answer 2

The point (2.33, 1.67) lie in the first quadrant.

Step-by-step explanation:

Given:

The two points on the line are (8, -9) and (2, 3).

Let the point that divides the line in the ratio 1 : 2 internally be $(x,y)$.

From section formula, we know that:

$x=\frac{mx_2+nx_1}{m+n}\\y=\frac{my_2+ny_1}{m+n}$

Here, $(x_1,y_1)=(8,-9),(x_2,y_2)=(2,3),m=1,n=2$

Therefore, the coordinates of the point are:

$x=\frac{1\times -9+2\times 8}{1+2}=\frac{-9+16}{3}=\frac{7}{3}=2.33\\y=\frac{1\times 3+2\times 1}{1+2}=\frac{3+2}{3}=\frac{5}{3}=1.67$

Therefore, the point is (2.33, 1.67)

Both these points are positive. So, both lie in the first quadrant.