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dexar [7]
2 years ago
15

given the points A(-3,-5) and B (5,0), find the coordinates of the point P on a directed line segment AB that partitions AB in t

he ratio 2:3
Mathematics
2 answers:
Sonja [21]2 years ago
8 0

\bf ~~~~~~~~~~~~\textit{internal division of a line segment} \\\\\\ A(-3,-5)\qquad B(5,0)\qquad \qquad \stackrel{\textit{ratio from A to B}}{2:3} \\\\\\ \cfrac{A\underline{P}}{\underline{P} B} = \cfrac{2}{3}\implies \cfrac{A}{B} = \cfrac{2}{3}\implies 3A=2B\implies 3(-3,-5)=2(5,0)\\\\[-0.35em] \rule{31em}{0.25pt}\\\\ P=\left(\frac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \frac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)\\\\[-0.35em] \rule{31em}{0.25pt}


\bf P=\left(\cfrac{(3\cdot -3)+(2\cdot 5)}{2+3}\quad ,\quad \cfrac{(3\cdot -5)+(2\cdot 0)}{2+3}\right) \\\\\\ P=\left( \cfrac{-9+10}{5}~~,~~\cfrac{-15+0}{5} \right)\implies P=\left(\frac{1}{5}~,~-3  \right)

marysya [2.9K]2 years ago
6 0

Answer:

(\frac{1}{5},-3).

Step-by-step explanation:

We have been given the coordinates of points A(-3,-5) and B (5,0). We are asked to find the coordinates of the point P on a directed line segment AB that partitions AB in the ratio 2:3.  

We will use section formula to solve our given problem. When a point P divides a line segment internally in ratio m:n, then coordinates of point P are:

[x=\frac{m\cdot x_2+n\cdot x_1}{m+n};y=\frac{m\cdot y_2+n\cdot y_1}{m+n}]

Upon substituting coordinates of our given points in section formula we will get,

[x=\frac{2\cdot 5+3\cdot -3}{2+3};y=\frac{2\cdot 0+3\cdot -5}{2+3}]

[x=\frac{10-9}{5};y=\frac{0-15}{5}]

[x=\frac{1}{5};y=\frac{-15}{5}]

[x=\frac{1}{5};y=-3]

Therefore, the coordinates of point P are (\frac{1}{5},-3).

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A cup has the format of a cylinder with a open top. The surface area of the cup is given by the area of it's base (a circle) and the area of it's walls, wich can be seen as rectangle where the width is the length of the circle at the base and the height is the height of the cylinder. So we have:

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