Name: Coordinates of Centroid
Uploaded: 2019-07-19
Duration: 3 min 16 s
Description: This video discusses how we can find the coordinates of the centroid using the coordinates of the three vertices given. Watch and learn the concept.

Question

Find the ratio in which the point

P (\frac{3}{4}, \frac{5}{12})

divides the line segment joining the points

A (\frac{1}{2}, \frac{3}{2})

and

B (2, - 5)

.

Accepted Answer

Let $P (\frac{3}{4}, \frac{5}{12})$ divide AB internally in the ratio m: n.

Using the section formula, we get

$(\frac{3}{4}, \frac{5}{12}) = (\frac{2 m - \frac{n}{2}}{m + n}, \frac{- 5 m + \frac{3}{2} n}{m + n})$

[ $∵$ internal section formula, the coordinates of point P divides the line segment joining the point $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ in the ratio $m_{1} : m_{2}$ internally is $(\frac{m_{2} x_{1} + m_{1} x_{2}}{m_{1} + m_{2}}, \frac{m_{2} y_{1} + m_{1} y_{2}}{m_{1} + m_{2}})$ ]

On equating, we get

$\frac{3}{4} = \frac{2 m - \frac{n}{2}}{m + n}$ and $\frac{5}{12} = \frac{- 5 m + \frac{3}{2} n}{m + n}$

$\Rightarrow \frac{3}{4} = \frac{4 m - n}{2 (m + n)}$ and $\frac{5}{12} = \frac{- 10 m + 3 n}{2 (m + n)}$

$\Rightarrow \frac{3}{2} = \frac{4 m - n}{m + n}$ and $\frac{5}{6} = \frac{- 10 m + 3 n}{m + n}$

$\Rightarrow 3 m + 3 n = 8 m - 2 n$ and $5 m + 5 n = - 60 m + 18 n$

$\Rightarrow 5 n - 5 m = 0$ and $65 m - 13 n = 0$

$\Rightarrow n = m$ and $13 (5 m - n) = 0$

Since, $m = n$ does not satisfy.

$∴ 5 m - n = 0$

$\Rightarrow 5 m = n$

$∴ \frac{m}{n} = \frac{1}{5}$

Hence, the required ratio is `1: 5`

Find the ratio in which the point $P (\frac{3}{4}, \frac{5}{12})$ divides the line segment joining the points $A (\frac{1}{2}, \frac{3}{2})$ and $B (2, - 5)$ .

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Find the ratio in which the point P34,512 divides the line segment joining the points A12,32 and B2, -5.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

Find the ratio in which the point $P (\frac{3}{4}, \frac{5}{12})$ divides the line segment joining the points $A (\frac{1}{2}, \frac{3}{2})$ and $B (2, - 5)$ .