Question

Find the cordinats of a point ponthe line segment janing A(1 2) and b(6 7) in sach way that ap²₅ab​

Answer 1

Explanation:

To find a point P on the line segment joining A(1, 2) and B(6, 7) such that the ratio of the squares of the lengths AP and PB is 25 (AP²/PB² = 25), you can use the concept of section formula.

Let the coordinates of point P be (x, y).

The section formula states:

If a line segment AB is divided by a point P(x, y) such that AP²/PB² = k², then:

x = (k * Bx + Ax) / (k + 1)

y = (k * By + Ay) / (k + 1)

In this case, we want AP²/PB² = 25, so k² = 25, and k = 5 (since we take the positive value).

Now, we can use the formula to find the coordinates of point P:

x = (5 * 6 + 1) / (5 + 1) = (30 + 1) / 6 = 31/6

y = (5 * 7 + 2) / (5 + 1) = (35 + 2) / 6 = 37/6

So, the coordinates of point P are (31/6, 37/6).