1.

Find the ratio in which the line segment joining the points (2,4,5) and (3,5,-4) is divided by the XY-plane ?​

Answer»

\underline{\textsf{GIVEN:}}

\textsf{Points are (2,4,5) and (3,5,-4)}

\underline{\textsf{TO FIND:}}

\textsf{The ratio in which the line segment joining the given points is divided by xy plane}

\underline{\textsf{SOLUTION:}}

\underline{\textsf{CONCEPT USED:}}

\boxed{\begin{minipage}{9cm}$\\\;\;\textsf{The co ordinates of the point which divides the line segment}\\\\\mathsf{joining\;(x_1,y_1,z_1)\;and\;(x_2,y_2,z_2)\;internally\;in\;the\;ratio \;m:n}\\\\\mathsf{are\;\;\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n},\dfrac{mz_2+nz_1}{m+n}\right)}\\$\end{minipage}}

\textsf{Let P be the point which divides the line segment joining (2,4,5)}

\textsf{and (3,5,-4) interrnally in the ratio m:n)}

\textsf{Then, co-ordinates of P are}

\mathsf{\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n},\dfrac{mz_2+nz_1}{m+n}\right)}

\mathsf{\left(\dfrac{m(3)+n(2)}{m+n},\dfrac{m(5)+n(4)}{m+n},\dfrac{m(-4)+n(5)}{m+n}\right)}

\mathsf{\left(\dfrac{3m+2n}{m+n},\dfrac{5m+4n}{m+n},\dfrac{-4m+5n}{m+n}\right)}

\textsf{Since the line segment joining the given points is divided by xy plane,}

\textsf{z component of P is zero}

\implies\mathsf{\dfrac{-4m+5n}{m+n}=0}

\implies\mathsf{-4m+5n=0}

\implies\mathsf{4m=5n}

\implies\mathsf{\dfrac{m}{n}=\dfrac{5}{4}}

\implies\boxed{\mathsf{m:n=5:4}}

\underline{\textsf{FIND MORE:}}

In what ratio is the line segment joining A(2,-3)&B(5,6) divided by x-axis ALSO find the COORDINATE of the point of division.

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Find the ratio in which the line segment joining the points (- 2 3) and (3 - 2) is divided by y axis​

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Find the ratio in which the line segment joining the points (-3,10), and(6,-8) is divided by(-1,6)​

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