Question

If A(3,7) and B(7,9) are two ends of a line segment which is divided by point Q in the ratio 3:4 , then find the co-ordinates of point Q.

• A. $(\frac{33}{7},\frac{55}{7})$
• B. $(\frac{22}{7},\frac{35}{7})$
• C. $(\frac{55}{7},\frac{25}{7})$
• D. $(\frac{32}{7},\frac{15}{7})$

Answer 1

The correct option is A $(\frac{33}{7},\frac{55}{7})$

The equation for the point that divides a line segment, joining the points $(x_1,y_1)and(x_2,y_2)$ in the ratio m : n is: $(\frac{(n\times x_1+m\times x_2)}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

Here,
$(x_1,y_1)=(3,7)$
$(x_2,y_2)=(7,9)m:n=3:4$

Hence, according to Section Formula:
$x=\frac{m{x}_2+n{x}_1}{m+n}=\frac{3\times 7+4\times 3}{3+4}=\frac{33}{7}$
$y=\frac{m{y}_2+n{y}_1}{m+n}=\frac{3\times 9+4\times 7}{3+4}=\frac{55}{7}$

$\therefore$ Co-ordinates of Q are $(\frac{33}{7},\frac{55}{7}).$