Question

7. The point which divides the line segment joining the points A(3,-2), and B(6, 7) internally in the ratio of 3 : 2 lies in which of the quadrants?

(A) I (B) II (C) III (D) IV

Please give an explanation, NO ABSURDNESS!​

Answer 1

Answer:

(A) I

Step-by-step explanation:

Required points:

$\frac{m_{1}x_{2}+m_{2}x_{1} }{m_{1}+m_{2} } ,\frac{m_{1}y_{2}+m_{2}y_{1} }{m_{1}+m_{2} }$

$\frac{2*3+3*6}{3+2} ,\frac{2*(-2)+3*7}{3+2}$

$\frac{6+18}{5} ,\frac{-4+21}{5}$

$\frac{24}{5} ,\frac{17}{5}$

The attached photo shows the signs of the four quadrants.

Quadrant I  is (+,+), so the point which divides the line segment joining the points A(3,-2), and B(6, 7) internally in the ratio of 3 : 2 lies in first quadrant.

So, the correct answer is option A.

If this helps, please mark me the brainliest. Thank you.

Answer 2

Given: A point divides the line segment joining the points A(3,-2), and B(6, 7) internally in the ratio of 3 : 2.

To find: Quadrant in which the point lies

Solution: The number line is divided into 4 quadrants.

In quadrant I, both x-coordinates and y-coordinates are positive.

In quadrant II, y-coordinates are positive but x-coordinates are negative.

In quadrant III, both x-coordinates and y-coordinates are negative.

In quadrant IV, x-coordinates are positive but y-coordinates are negative.

Here, A(3,-2) be (x1,y1) and B(6,7) be (x2,y2).

The ratio is given as 3:2.

Therefore, m = 3 and n=2

The coordinates of the point which divides the two points in ratio m:n is given by section formula:

(x,y) = mx2+nx1/m+n , my2+ny1 / m+n

= 3 × 6 + 2 × 3 / 2+3 , 3×7 + 2×-2 / 2+3

= 18+6/5, 21-4/5

= 24/5 , 17/5

The coordinates of the point which divides the points A and B is (24/5, 17/5).

Since both x-coordinate and y-coordinate is positive, the point lies in option (A) quadrant I.