Question

the point p(x,1) lies to divide (3,4) and (7,5)​

Answer 1

Answer:

If the point P (1/2, y) lies on the line segment joining the points A (3, -5) and B (-7, 9) then find the ratio in which P divides AB. Also, find the value of y.Read more on Sarthaks.com - https://www.sarthaks.com/163234/the-point-lies-the-line-segment-joining-the-points-and-then-find-the-ratio-which-divides-also

Step-by-step explanation:

this is the same method of this question

Answer 2

❍ Let P(x,y) be the point which divides the line segment internally.

★ Using the section formula for the internal division, i.e. -

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

Given:

• $\sf{m_1\:=\:3} \\ \sf{m_2\:=\:2} \\ \sf{(x_1,\:y_1)\:=\:(2,\:-1)} \\ \sf{(x_2,\:y_2)\:=\:(-3,\:4)}$

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Putting the above values in the above formula, we get :

$\:\Longrightarrow\:\sf{(x,y)\:=\:{\dfrac{3\:(-3)\:+\:2\:(2)}{3\:+\:2}}\:\:\:,\:\:\:{\dfrac{3\:(4)\:+\:2\:(-1)}{3\:+\:2}}}$

$\:\Longrightarrow\:\sf{(x,y)\:=\:{\dfrac{-9\:+\:4}{5}}\:\:\:,\:\:\:{\dfrac{12\:-\:2}{5}}}$

$\:\Longrightarrow\:\sf{(x,y)\:=\:{\dfrac{-5}{5}}\:\:\:,\:\:\:{\dfrac{10}{5}}}$

$\:\Longrightarrow\:\sf{(x,y)\:=\:-1\:\:\:,\:\:\:2}$

$\therefore {\underline{\sf{Hence,\:{\textsf{\textbf{(-1,\:2)}}}\:is\: the \:point \:which \:divides\: the\: line \:segment \:internally}}}$

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