Question

M and N are two points on the x-axis and y-axis, respectively. P(3,2) divides the line segment MN in the ratio 2:3. Find the coordinates of M and N.

(a) M(2,0),N(0,3)
(b) M(0,2),N(3,0)
(c) M(2,0),N(3,0)
(d) M(0,2),N(0,3)

Answer 1

The coordinates of points M and N are M(0,2) and N(3,0). The solution involves using the section formula with the given ratio to solve for the coordinates of M and N, leading to option (b) being correct.

Step-by-step explanation:

The student asked for help finding the coordinates of points M and N on the x-axis and y-axis, respectively, given that point P(3,2) divides the line segment MN in the ratio 2:3. To determine the coordinates of M and N, we must assume that since N is on the y-axis, its x-coordinate is 0, and since M is on the x-axis, its y-coordinate is 0.

Let M be (x,0) and N be (0,y). The coordinates of P can be found using the section formula in the ratio 2:3. As a result, the x-coordinate of P is (2x + 3*0) / (2+3) = 3 and the y-coordinate of P is (2*0 + 3y) / (2+3) = 2. Solving for x and y gives us x = 3 and y = 2. Therefore, M is (3,0) and N is (0,2).

The correct option that shows this result is (b) M(0,2), N(3,0). It coincides with our calculations as M has a y-coordinate of 2 while being on the x-axis, and N has an x-coordinate of 3 while being on the y-axis