Find the ratio in which P(4, m) divides the line segment joining the p

1.	Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) andB(6,-3). Hence find m.
Answer» 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 Like my answer if you find it useful!

Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) andB(6,-3). Hence find m.

Answer»

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

Like my answer if you find it useful!