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

it is exactly the correct answer

Answer 2

Answer:

The value of m is -4.

Step-by-step explanation:

If the point P(m,3) lies on the line segment joining the point A(-2/5,6),and B(2,8), then all these points are collinear and the slopes AB, AP, PB are same.

Slope formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Slope of AB is

$m_1=\frac{8-6}{2+\frac{2}{5}}=\frac{2}{\frac{12}{5}}=\frac{5}{6}$

The slope of PB is

$m_2=\frac{8-3}{2-m}=\frac{5}{2-m}$

$m_1=m_2$

$\frac{5}{6}=\frac{5}{2-m}$

$2-m=6$

$2-6=m$

$-4=m$

Therefore the value of m is -4.