Find the length of a segment with an endpoint of (2, 1) and a midpoint of (–2, –1).

Answer:Length of segment [tex]=4\sqrt5[/tex] units = 8.94 unitsStep-by-step explanation:Given:End point of line: (2,1)Midpoint of line: (-2,-1)To find length of line segment.Solution:Distance from endpoint to midpoint is half the length of segment as the midpoint divides the line into equal halves.Distance from end point to mid point can be found out using distance formula:[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2)[/tex]Plugging in points for end point (2,1) and midpoint(-2,-1).[tex]d=\sqrt{(-2-2)^2+(-1-1)^2)[/tex][tex]d=\sqrt{(-4)^2+(-2)^2)[/tex][tex]d=\sqrt{16+4)[/tex][tex]d=\sqrt{20}[/tex][tex]d=2\sqrt{5}[/tex]Length of half segment [tex]=2\sqrt{5}[/tex] units∴ Length of segment = [tex]2\times length\ of\ half\ segment= 2\times 2\sqrt5=4\sqrt5[/tex] units