Question

if the point C (-1,2) divideds internally the line segment joining A (2,5) and B in the ratio 3:4 find the coordinates of B​

Answer 1

Answer :-

The coordinates of B are (-5,-2).

Step-by-step explanation :-

∅ Let the coordinates of B be (x, y).

∅ The line segment is divided in the ratio 3 : 4.

∴ m$_1$ = 3 and m$_2$ = 4

∅ And ATP :

∴ (x1, y1) = (-1, 2) and (x$_1$, y$_1$) = (2, 5) and (x$_2$, y$_2$) = (x, y).

∅ Using Section formula :

(x1,y1) = $\bold{\frac{m_1x_2+m_2x_1}{m_1+m_2}},\bold{\frac{m_1y_2+m_2y_1}{m_1+m_2}}$

∅ Substituting we get :

(-1,2) = $\bold{\frac{3(x)+4(2)}{3+4},\frac{3(y)+4(5)}{3+4}}$

(-1) = $\bold{\frac{3x+8}{7}}$ and (2) = $\bold{\frac{3y+20}{7}}$

∅ So we get :

3x + 8 = -7

3x = -15

∴ x = -5

3y + 20 = 14

3y = -6

∴ y = -2

∴ The coordinates of B are (-5,-2).