Question

Find the coordinates of the point which divides the join of the points $(2,4)$ and $(6,8)$ externally in the ratio $5:3$.

• A. $(12,14)$
• B. $(14,12)$
• C. $(-12,14)$
• D. $(12,-14)$

Answer 1

The correct option is A $(12,14)$

Given $A(2,4)$ and $B(6,8)$

Applying the section formula externally,

$(\frac{L{x}_2-{mx}_1}{L-m},\frac{L{y}_2-{my}_1}{L-m})$

Here the ratio given is $5:3$ that is $L=5$ and $m=3$, therefore,

$(\frac{L{x}_2-{mx}_1}{L-m},\frac{L{y}_2-{my}_1}{L-m})=(\frac{(5\times 6)-(3\times 2)}{5-3},\frac{(5\times 8)-(3\times 4)}{5-3})$

$=(\frac{30-6}{2},\frac{40-12}{2})=(\frac{24}{2},\frac{28}{2})=(12,14)$

Hence, the coordinates of the point is $(12,14)$.