Respuesta :
[tex]\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}[/tex]
The distance between the two points (4,6) and (-2,9) is [tex]3\sqrt{5}[/tex] units.
What is distance?
It is the measurement done by ruler between two points on a surface.
How to calculate distance between points?
There are two points given which are (4,6) and (-2,9).
Distance between the two points can be calculated by the following formula:
Distance=[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
where x1, x2 ,y1,y2 are the points.
So, the distance between (4,6) and (-2,9) is
=[tex]\sqrt{(-2-4)^{2} +(9-6)^{2} }[/tex]
=[tex]\sqrt{(-6)^{2} + (3)^{2} }[/tex]
=[tex]\sqrt{36+9}[/tex]
=[tex]\sqrt{45}[/tex]
=[tex]3\sqrt{5}[/tex] units.
Hence the distance between (4,6) and (-2,9) is [tex]3\sqrt{5} units[/tex].
Learn more about distance at https://brainly.com/question/2854969
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