Question

Find the coordinates of the point which divides the join of (-1,7) and (4.-3) in the ratio 2:3 ??

Answer 1

Question:-

Find the coordinates of the point which divides the join of (-1,7) and (4,-3) in the ratio 2:3 ?

Solution:-

Let the given points be A(-1,7) and B(4,-3)

Now,

Let the point be P(x, y) which divides AB in the ratio 2:3

Here,

${ \bf x \: = \frac{m_1 x_2 \: + \: m_1 x_1}{m_1 \: + \: m_2}}$

Where,

$m_1$ = 2 , $m_2$ = 3

$x_1$ = -1 , $x_2$ = 4

$\therefore$ Putting values we get,

x = $\frac{2 \: × \: 4 \: + \: 3 \: × \: -1}{2 \: + \: 3}$

x = $\frac{8 \: - \: 3}{5}$

x = $\frac{5}{5}$

x = 1

Now,

Finding y

${ \bf y \: = \frac{m_1 y_2 \: + \: m_2 y_1}{m_1 \: + \: m_2}}$

Where,

$m_1$ = 2 , $m_2$ = 3

$x_1$ = 7 , $x_2$ = -3

$\therefore$ Putting values we get,

y = $\frac{2 \: × \: -3 \: + \: 3 \: × \: 7}{2 \: + \: 3}$

y = $\frac{-6 \: + \: 21}{5}$

y = $\frac{15}{5}$

y = 3

Hence x = 1, y = 3

So, the required point is P(x, y)

= P(1, 3)

The coordinates of the point is P(1, 3). [Answer]

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Note:- Refer the attachment.

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