Question

Coordinates of the points which divides the join of $(-1,7)$ and $(4,-3)$ in the ratio $2:3$ are $(1,3).$

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient

Answer 1

The correct option is A True

We know that, the coordinates of the point dividing the line segment joining the points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ in the ratio m:n is given by $(\frac{m_1{x}_2+m_2{x}_1}{m_1+m_{2}1},\frac{m_1{y}_2+m_2{y}_1}{m_1+m_2})$
Given $(x_1,y_1)=(-1,7)$; $(x_2,y_2)=(4,-3)$
$(m_1,m_2)=2:3$
Coordinates of point of intersection of line segment is
$(\frac{\left(2\right)\left(4\right)+\left(3\right)(-1)}{2+3},\frac{\left(2\right)(-3)+\left(3\right)\left(7\right)}{2+3})$
$=(5/5,15/5)$
$=(1,3)$