Question

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

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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 \: = (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 =
`(2 \: × \: 4 \: + \: 3 \: × \: -1)/(2 \: + \: 3)`

x =
`(8 \: - \: 3)/(5)`

x =
`(5)/(5)`

x = 1

Now,

Finding y

`{ \bf y \: = (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 =
`(2 \: × \: -3 \: + \: 3 \: × \: 7)/(2 \: + \: 3)`

y =
`(-6 \: + \: 21)/(5)`

y =
`(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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