Question

The coordinates of the point which divides the line segment joining (4, –3) and (9, 7) in the ratio 3 : 2 externally is .

• A. (19, 27)
• B. (7, 3)
• C. (35, 15)
• D. $(\frac{19}{5},\frac{27}{5})$

Answer 1

The correct option is A (19, 27)

Let A(4, -3), B(9, 7) be the points
and C divides AB externally in the
ratio 3 : 2.

$\mathrm{So},\mathrm{by}\mathrm{using}\mathrm{section}\mathrm{formula}\mathrm{for}\mathrm{external}\mathrm{division}\mathrm{between}\mathrm{two}\mathrm{points}A\left(x_1,y_1\right)\mathrm{and}B\left(x_2,y_2\right),\mathrm{the}\mathrm{point}\mathrm{of}\mathrm{division}\mathrm{has}\mathrm{the}\mathrm{coordinates}(\frac{m{x}_2-n{x}_1}{m-n},\frac{m{y}_2-n{y}_1}{m-n})\therefore CoordinatesofCwillbe(\frac{3\times 9-2\times 4}{3-2},\frac{3\times 7-2\times \left(-3\right)}{3-2})=\left(19,27\right)$