Question

If the point P(x,3) divides the line joining the points (3, 13) and (-1,-4) Find the ratio coordinates of dividing point P.

Answer 1

The point P divides the line segment in the ratio of 7:10. By applying the section formula, the ratio coordinates of P are found to be (-0.5, 3).

Step-by-step explanation:

To find the ratio coordinates of the dividing point P which divides the line segment joining the points A(3, 13) and B(-1, -4), we will use the section formula. Since the y-coordinate of P is given as 3, we can find the ratio in which P divides the line segment AB.

Let P(x, 3) divide AB in the ratio k:1. The section formula then gives us the coordinates of P in terms of k as follows:

x = (k*(-1) + 1*3) / (k + 1)
3 = (k*13 + 1*(-4)) / (k + 1)

Solving the second equation for k, we get:

3(k + 1) = k*13 - 4
3k + 3 = 13k - 4
10k = 7
k = 7/10

So the ratio required is 7:10. Now, we can use this value of k to find the x-coordinate.

x = (7*(-1) + 1*3) / (7 + 1)
x = (-7 + 3) / 8
x = -4 / 8
x = -0.5

Hence, the coordinates of P are (-0.5, 3) and it divides AB in the ratio 7:10.