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lesya [120]
3 years ago
5

3 points lie on an xy plane, with each point representing where a particular person lives. Amy lives at point (2,3); Brian lives

at point (0,7); and Claire lives at point (-2,3). They all wish to meet up with each other for lunch, but at a location that is equidistant from each of their respective houses. At what point do they meet?
Mathematics
1 answer:
geniusboy [140]3 years ago
6 0
The equidistant point for all three, will be the "centroid" of their triangular locations
thus \bf \textit{Centroid of a Triangle}
\begin{array}{llll}
Amy
\begin{array}{llll}
(2,3)\\
x_1,y_1
\end{array}\quad Brian
\begin{array}{llll}
(0,7)\\
x_2,y_2
\end{array}\quad Claire
\begin{array}{llll}
(-2,3)\\
x_3,y_3
\end{array}\\ \quad \\\\\\
\left(\cfrac{x_1+x_2+x_3}{3}\quad ,\cfrac{y_1+y_2+y_3}{3}\quad \right)
\end{array} 

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Answer:

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Step-by-step explanation:

x^{2}  - 9x +10\\

The easiest way to factor is to find two numbers of the "a" value (the coefficient before x^{2}) and the factors of the c value (10) that ADD up to give you -9, in this case it would be:

1          -10  --> 1(-10) gives you -10

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adding these together -10 + (-1) = -11 which does not equal -9.

You could stop here and conclude that this is not factorable by inspection.

Another method: using the quadratic formula to find its roots.

Roots: (\frac{9-\sqrt{41} }{2}, 0) and (\frac{9+\sqrt{41}}{2}, 0)

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