Considering the definition of distance between two points, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
The distance between two points is equal to the length of the segment that joins them. Therefore, to determine the distance between two different points, you must calculate the squares of the differences between their coordinates and then find the root of the sum of said squares.
In other words, the distance between two points in space is the magnitude of the vector formed by said points.
So, given the coordinates of two distinct points (x1, y1) and (x2, y2), the distance between two points is the square root of the sum of the squares of the difference of the coordinates of the points:
distance= [tex]\sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]
In this case, you know:
Replacing in the definition of distance:
distance= [tex]\sqrt{(5-(-2))^{2} +(-4-1)^{2} }[/tex]
distance= [tex]\sqrt{(5+2)^{2} +(-5)^{2} }[/tex]
distance= [tex]\sqrt{7^{2} +(-5)^{2} }[/tex]
distance= [tex]\sqrt{49+25 }[/tex]
distance= √74= 8.6023
Finally, the distance between the points (-2,1) and (5,-4) is √74= 8.6023.
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