Question

Only for Brainly moderators , Brainly stars and brainly best users ▬▬▬▬ஜ۩۞۩ஜ▬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

Answer:

The value of m is -4.

Step-by-step explanation:

Given :

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

To find :

the value of m

Solution :

The points p, a and b lie on the line segment. They are collinear.

The area enclosed by collinear points is 0.

Area of the triangle is given by,

$\tt \triangle = \dfrac{1}{2}|x_1 (y_2 - y_3) + x_2 (y_3 - y_1) + x_3 (y_1 - y_2) |$

Put,

x₁ = m ; y₁ = 3

x₂ = -2/5 ; y₂ = 6

x₃ = 2 ; y₃ = 8

_____________

0 = ½ | m(6 - 8) + (-2/5) (8 - 3) + 2(3 - 6) |

0 = ½ | m(-2) - 2/5(5) + 2(-3) |

0 = ½ | -2m - 2 - 6 |

0 = -2m - 2 - 6

0 = -2m - 8

-2m = 8

m = 8/-2

m = -4

Therefore, the value of m is –4.

Answer 2

Answer:

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

Step-by-step explanation:

means points , P, a and b are collinear.

so, area enclosed by points P , a and b = 0

use formula ,

Δ = 1/2 [ x₁ (y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) ]

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