Find the midpoint between points (-4,2) and (2,-2) (1,-1) (0,-1) (-1,0) (1,0)

1 answer:

3 0

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
(\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad 
(\stackrel{x_2}{2}~,~\stackrel{y_2}{-2})
\qquad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
\left( \cfrac{2-4}{2}~~,~~\cfrac{-2+2}{2} \right)\implies \left( \cfrac{-2}{2}~~,~~\cfrac{0}{2} \right)\implies (-1~,~0)$

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Step-by-step explanation:

0) the basic formula is: L=v*t, where L - distance, v - speed/velocity; t - time;

1) if the person's speed in still water is 'v' and the speed of water is 5 (according to the condition), then the upstream speed is 'v-5' and the downstream speed is 'v+5';

2) according to the condition the upstream time and the downstream time are the same, it means t₁=t₂=t, where t₁=upstream time and t₂=downstream time;

3) according to the items above it is possible to make up the equation of the upstream travel: t(v-5)=3; ⇒ t=3/(v-5);

4) according to the items above it is possible to make up the equation of the downstream travel: t(v+5)=13; ⇒ t=13/(v+5);

5) if t=3/(v-5) and t=13/(v+5), then

$\frac{3}{v-5} =\frac{13}{v+5}; \ => \ v=8.$