Question

The point C (-1, 2) divides the line segment AB joining the points A (2, 5) and B (α, β) in the ratio 3:4. Find the values of α, β and hence the coordinates of B.

Answer 1

Answer:

Given points :- A(x1,y1) =(2,5), B(x2,y2) =(alpha ,beta )

Given ratio(m:n) :- 3:4

Using the formula

$Ģ = ( \frac{mx2+nx1 }{m + n} , \frac{my2+ny1 }{m + n} )$

$(3,4) = ( \frac{3 \alpha + 8}{7} , \frac{3 \beta + 20}{7} )$

$3 = \frac{3 \alpha + 8}{7} \: and \: 4 = \frac{3 \beta + 20}{7}$

Hope you can obtain (alpha and beta )