Question

If the point C(–1, 2) divides internally the line segment joining A(2, 5) and B in ratio 3 : 4 find the coordinates of B

Answer 1

$\huge\bold {ANSWER}$

Let the coordinates of point A be$(x_1,y&1)$

And the coordinates of point B be$(x_2,y_2)$

and the point dividing the line be P with its coordinates be (x=-1, y=2) .

And the ration in which they are divided be m1 = 3 and m2 =5.

So, by section Formula we know,

y=$\frac{m_1 \times y_2+ m_2 \times y_1}{m_1 +m_2}$

2 =$\frac{3 \times y_2 + 5 \times 5}{3+5}$

On cross multiplication,

$16=3 y_2 - 25$

$9 =3 y_2$

$\frac{9}{3} = y2$

So, the y coordinate of B is 3.

So, to find x,

X=$\frac{m_1 \times x_2 + m_2 \times x_1}{m1 +m_2}$

-1=$\frac{3 \times x_2 + 5 \times 2}{7+6}$

On cross multiplication,

$-8 = 3 x_2 + 10$

$-8 + (-10) =3 x_2$

$-18 =3 x_2$

$\frac{-18}{3} = x_2$

$-6= x_2$

So, the x coordinate of B is -6.

Therefore the coordinates of B are (3,-6).