Question

The coordinates of a point A which divides the line segment joining the points P(1,3) and Q(3, 4) internally in the ratio 3 : 4 can be​

Answer 1

Answer:

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Answer 2

Given. The point $A$ divides the line segment joining the points $P(1,3)$ and $Q(3,4)$ internally in the ratio $3:4$.

To find. The coordinates of $A$

Formula. If the join of $(x_{1},y_{1})$ and $(x_{2},y_{2})$ be divided into the ratio $m:n$ internally at a point $P$, then the coordinates of the point $P$ be

$\quad (\frac{nx_{1}+mx_{2}}{m+n},\frac{ny_{1}+my_{2}}{m+n})$.

Solution.

• Here given points are $P(1,3)$ and $Q(3,4)$

• Ratio of internal division by $A$ is $3:4$

• Using Formula, we find the coordinates of the point $A$ as follows,
• $\quad (\frac{4.1+3.3}{3+4},\frac{4.3+3.4}{3+4})$
• $\Rightarrow (\frac{4+9}{7},\frac{12+12}{7})$
• $\Rightarrow (\frac{13}{7},\frac{24}{7})$

Answer.

Coordinates of $A$ are $(\frac{13}{7},\frac{24}{7})$