Here, given points are A(-3, 1) and B(-8, 9) and let the point dividing the line joining two points be C(-6,a).
Let the ratio be m:n
By section formula,
x = \(\frac{mx_2+mx_1}{m+n}\), y = \(\frac{my_2+ny_1}{m+n}\)
For point C(-6,a),
- 6 = \(\frac{m\times(-8)+n\times(-3)}{m+n}\) ...…(1)
And a = \(\frac{m\times9+n\times1}{m+n}\) .…...(2)
Solving 1 for finding ratio between m and n,
- 6 = \(\frac{m\times(-8)+n\times(-3)}{m+n}\)
-6 (m + n) = -8m -3n
6m + 6n = 8m + 3n
∴ 2m = 3n
∴ \(\frac{m}n\) = \(\frac{3}2\)
∴ m : n = 3 : 2
Now solving for equation 2, where m = 3 and n = 2
a = \(\frac{m\times9+n\times1}{m+n}\)
a = \(\frac{3\times9+2\times1}{3+2}\)
∴ a = \(\frac{27+2}5\)
∴ a = \(\frac{29}5\)
∴ value of a is \(\frac{29}5\)
