Here, given points are A ( -3,10) and B(6, -8) and the point dividing the line joining two points is P(-1,y).
Let the ratio be m:n
By section formula,
x = \(\frac{mx_2+nx_1}{m+n}\), y = \(\frac{my_2+ny_1}{m+n}\)
For point P(-1,a),
Solving 1 for finding ratio between m and n,
-1 = \(\frac{m\times6+n\times(-3)}{m+n}\)
- (m + n) = 6m -3n
m + n = -6m + 3n
∴ 7m = 2n
∴ \(\frac{m}n\) = \(\frac{2}7\)
∴ m : n = 2 : 7
Now solving for equation 2, where m = 2 and n = 7
y = \(\frac{m\times(-8)+n\times10}{m+n}\)
y = \(\frac{2\times(-8)+7\times10}{2+7}\)
∴ y = \(\frac{-16+20}9\)
∴ y = \(\frac{54}9\)
∴ value of y is 6
