Find the distance between the two points in simplest radical form (4,6) and (-2,9)

1 answer:

6 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{9})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d = \sqrt{(-2-4)^2+(9-6)^2}\implies d = \sqrt{(-6)^2+3^2}\implies d = \sqrt{36+9} \\\\\\ d = \sqrt{45}\implies d = \sqrt{9\cdot 5}\implies d=\sqrt{3^2\cdot 5}\implies d = 3\sqrt{5}$

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x^2 + y^2 > 7^2

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From the other equation, we would get:

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This is parabola, anything that is in the graph of the parabola or below will be a solution for this inequality.

Then the solutions of the system, are the ones that are in the region of solutions for both inequalities.

You can see the graph below, where both regions are graphed. The intersection of these regions is the region of the solutions for the system of inequalities:

by looking at the graph, we can see a lot of points that are solutions, like:

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(2, -10)

etc.