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3 years ago

Find the point that is two-thirds of the way from (3,4) to (9,-2)

Mathematics

1 answer:

hoa [83]3 years ago

4 0

Keeping in mind that, the segment is split in three thirds, and the point is 2/3 of the way, so is closer to (9, -2), with a 2:1 ratio, check the picture below.

$\bf \left. \qquad \right.\textit{internal division of a line segment}
\\\\\\
A(3,4)\qquad B(9,-2)\qquad
\qquad 2:1
\\\\\\
\cfrac{AC}{CB} = \cfrac{2}{1}\implies \cfrac{A}{B} = \cfrac{2}{1}\implies 1A=2B\implies 1(3,4)=2(9,-2)\\\\
-------------------------------\\\\
{ C=\left(\cfrac{\textit{sum of "x" values}}{\textit{sum of ratios}}\quad ,\quad \cfrac{\textit{sum of "y" values}}{\textit{sum of ratios}}\right)}\\\\
-------------------------------$

$\bf C=\left(\cfrac{(1\cdot 3)+(2\cdot 9)}{2+1}\quad ,\quad \cfrac{(1\cdot 4)+(2\cdot -2)}{2+1}\right)
\\\\\\
C=\left( \cfrac{3+18}{3}~~,~~\cfrac{4-4}{3} \right)\implies C=\left( 7~~,~~0 \right)$

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3 years ago

-x=-15 Syep by step solution need

andrew-mc [135]

Answer:

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2 years ago

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Please help me!! Will get brainliest!

makvit [3.9K]

Completing the square follows the principle of taking $a x^{2} +bx+c$ and converting it into $(x+ \frac{b}{2})^2+d$ where d is the 'correctional number' as I like to call it - i.e. the number that converts the expanded bracket into the +c, since the expanded bracket will give us $a x^{2} +b$ .

In this case, 2/2=1 so we have the first part: $(w+1)^2$ .
Expanding this gives us $w^2+2w+1$ . We need c to be 9, so we can just add 8.
Putting this together:

$w^2+2w+9=(w+1)^2+8$

Now we can solve it more easily.
Rearranging:
$(w+1)^2=-8 \\ w+1= +-\sqrt{-8} = +-\sqrt{8}i=+-2 \sqrt{2}i \\ \boxed{w=-1+ 2\sqrt{2}i\ or\ -1-2 \sqrt{2}i }$

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