If the Point P(m,3) lies on the line segment joining the points A(-2/5,6) and B(2,8),find the value of m - Maths - Coordinate Geometry

Question

If the Point P(m,3) lies on the line segment joining the
points A(-2/5,6) and B(2,8),find the value of m

Kirthiga Suresh · Accepted Answer

Since the line segment connects the points $A (- \frac{2}{5}, 6), B (2, 8)$ ,

equation of the line segment is given by:

$\frac{y - 6}{x - (- \frac{2}{5})} = \frac{8 - 6}{2 - (- \frac{2}{5})} = \frac{2}{2 + \frac{2}{5}}$

$\frac{y - 6}{x + \frac{2}{5}} = \frac{2}{2 + \frac{2}{5}} = \frac{2}{\frac{12}{5}}$

$\frac{y - 6}{\frac{(5 x + 2)}{5}} = \frac{5}{12} \times 2 = \frac{5}{6}$

$\frac{5 (y - 6)}{5 x + 2} = \frac{5}{6}$

$\frac{y - 6}{5 x + 2} = \frac{1}{6}$

$6 y - 36 = 5 x + 2$

$\Rightarrow x = \frac{6 y - 38}{5}$

Since the point $P (m, 3)$ lies on the line segment connecting points A and B,

$m$ is given by:

$m = \frac{6 \times 3 - 38}{5} = \frac{18 - 38}{5} = - 4$

Hence, $m = - 4$

If the Point P(m,3) lies on the line segment joining the points A(-2/5,6) and B(2,8),find the value of m.