Question

determine the ratio in which the point P (M, 6) divides the join of A (- 4,3) and B (2,8) also find the values of m

Answer 1

3-6/-4-M=8-3/2-(-4)
-3/4M=5/4

4and4 gets cancelled ...and
M=3+5
=8..
M=8

Answer 2

The two points joining make a line segment AB.

The coordinates of A are (-4,3) and B (2,8)

P has unknown x coordinate and y coordinate as 6.

P divides the line segment AB in the ratio (k:1) (say)

Then by ratio formula, coordinates of P is

$A (- 4,3) and B (2,8)</p><p>=(\frac{2k-4}{k+1} ,\frac{8k+3}{k+1})$

Since y coordinate is given as 6, equate to 6 to solve for k.

$\frac{8k+3}{k+1}=6:</p><p>6k+6 = 8k+3:</p> <p>k=2/3</p> <p>Ratio = 2:3$

M = x coordinate of P =$\frac{2k-4}{k+1}= \frac{\frac{4}{3}-4 }{\frac{5}{3} } </p><p>= \frac{-8}{5}$