Question

Find the ratio in which the point P(4,m) divides the line segment joining the points A(2,3) and B(6,-3).

Answer 1

Heya !!

Let the ratio be k : 1

By section formula

(x, y) = [ (kx2 + x1) / (k + 1) , (ky2 + y1) / (k + 1) ]

(4, m) = [ {k(6) + 2} / (k + 1) , {k(–3) + 3} / (k + 1) ]

4 = (6k + 2) / (k + 1) and m = (–3k + 3) / (k + 1)

=> 4k + 4 = 6k + 2

=> 6k – 4k = 4 – 2

=> 2k = 2

=> k = 1

Now, substituting k = 1 in m's value

m = [–3(1) + 3] / (1 + 1)

=> –3+3 / 2

=> 0 / 2

=> 0

Answer 2

Reder the attachment.