Question

If a point p(m,3) lies on the line segment joining the point a(-2/5,6),and b(2,8) find the value of m

Answer 1

HEY MATE HERE IS YOUR ANSWER....

Answer 2

a point P(m, 3) lies on the line segment joining the point a (-2/5, 6) and b(2,8).

means points , P, a and b are collinear.
so, area enclosed by points P , a and b = 0
use formula ,
$ar\Delta=\frac{1}{2}[x_1(y_2-y_3)+x_2(y_2-y_3)+x_3(y_3-y_1)]$

so, area enclosed by points P, a and b = ∆Pab
∆Pab = 1/2 {m(6 - 8) + (-2/5)(8 - 3) + 2(3 - 6)}
0 = -2m - 2 - 6
0 = -2m - 8
m = -4

hence m = -4