Question

Find the co-ordinates of point P if P divides the line segment

joining the points A (–1, 7) and B (4, –3) in the ratio 2:3.​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given:

• Co - ordinates of point A = (-1 , 7)
• Co - ordinates of point B = (4, - 3)
• Ratio in which P divides A and B is 2:3.

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To find:

• Co - ordinates of point P ?

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Solution:

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☯ Let coordinates of point P be (x,y).

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$\dag\;{\underline{\frak{Using\;section\;formula\;:}}}$

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$\star\;{\boxed{\sf{\purple{(x,y) = \bigg( \dfrac{m_2 x_1 + m_1 x_2}{m_1 + m_2}\;,\; \dfrac{m_2 y_1 + m_1 y_2}{m_1 + m_2} \bigg)}}}}$

$\dag\;{\underline{\frak{Putting\;values,}}}$

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$:\implies\sf (x,y) = \bigg( \dfrac{3 \times (-1) + 2 \times 4}{2 + 3}\;,\; \dfrac{3 \times (7) + 2 \times (-3)}{2 + 3} \bigg)$

$:\implies\sf (x,y) = \bigg( \dfrac{8 - 3}{5}\;,\; \dfrac{-6 + 21}{5}\bigg)$

$:\implies\sf (x,y) = \bigg( \dfrac{5}{5}\;,\; \dfrac{15}{5}\bigg)$

$:\implies\sf \pink{(x,y) = (1 , 3)}\;\bigstar$

$\therefore\;{\underline{\sf{Thus,\; Coordinates\;of\;point\;P\;are\; {\textsf{\textbf{(1,3)}}}.}}}$

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$\qquad\qquad\boxed{\bf{\purple{\mid{\overline{\underline{\bigstar\:More\;to\;know:}}}}\mid}}$

Formula that is used to find the distance between two points :

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• Distance Formula = $\sf \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$