Math, asked by 096sstrishitha, 2 months ago

Find the co ordinates of the points which divides the line segment of the points (-1,7) and (4,-3) in the ratio 2:3 using section formula​

Answers

Answered by ShírIey
67

Given: The Co – ordinates of the Points which are dividing the line segment of the points (–1, 7) and (4, – 3) in the ratio of 2: 3.

Need to find: The Co – ordinates?

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\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}\\⠀⠀⠀⠀

✇ To Calculate the coordinates of the point dividing the line segment joining the points (x₁ , y₁) and (x₂, y₂) in the ratio of m: n, Section formula is Given by :

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\quad\star\;\underline{\boxed{\sf{\Big(x, y\Big) = \Bigg(\dfrac{m_1 x_2 + m_2 x_1}{m_1 + m_2}\Bigg), \Bigg(\dfrac{m_1 y_2 + m_2 y_1}{m_1 + m_2}\Bigg)}}}\\\\

\sf{We\;have}\begin{cases}\sf{ \:  \: m_1:m_2 = \bf{2: 3}}\\\sf{ \:  \: (x_1, y_1)= \bf{(-1, 7)}}\\\sf{ \:  \: (x_2, y_2)= \bf{(4, -3)}}\end{cases}\\\\

\qquad\underline{\bf{\dag} \:\mathfrak{Substituting \;values\;in\;formula\; :}}\\\\⠀⠀⠀⠀

:\implies\sf \Bigg(\dfrac{(2)(4) + 3(-1)}{2 + 3}, \dfrac{(2)(-3) + (3) (7)}{2 + 3}\Bigg) \\\\\\:\implies\sf \Bigg(\dfrac{8 + (-3)}{5}, \dfrac{-6 + 21}{5}\Bigg)\\\\\\:\implies\sf \cancel{\dfrac{ \: 5 \: }{ \: 5 \: }, \:  \dfrac{ \: 15 \: }{ \: 5 \: }}\\\\\\:\implies\underline{\boxed{\pmb{\frak{ \purple{(1, 3)}}}}}\;\bigstar\\\\

\therefore{\underline{\textsf{Hence, the required co-ordinates are \textbf{(1, 3)}.}}}

Answered by Itzheartcracer
25

Given :-

Point - (-1,7) and (4,-3)

Ratio = 2:3

To Find :-

Coordinate

Solution :-

We know that

\sf P(x,y)=\bigg\lgroup\dfrac{m_1x_2+m_2x_1}{m_1 + m_2},\dfrac{m_1y_2+m_2y_1}{m_1+m_2}\bigg\rgroup

We have

\sf \bigg\lgroup\dfrac{2\times 4 + 3\times -1}{2+3},\dfrac{2\times -3+ 3\times7}{2+3}\bigg\rgroup

\sf\bigg\lgroup\dfrac{8+(-3)}{5},\dfrac{(-6)+21}{5}\bigg\rgroup

\sf\bigg\lgroup \dfrac{8-3}{5},\dfrac{-6 + 21}{5}\bigg\rgroup

\sf\bigg\lgroup \dfrac{5}{5},\dfrac{15}{5}\bigg\rgroup

\sf 1,3

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