Answer:
[tex]\textbf{The length of the line segment is $26$ units.}\\[/tex]
Step-by-step explanation:
[tex]\textup{Given one endpoint and the midpoint of the line segment.}\\The mid point formula is: $ M = \left( \frac{x_1 + x_2}{2} \right ) + \left ( \frac{y_1 + y_2}{2} \right ) $ \\Now call $(x_1,y_1) = (0,-1)$\& $M = (12,4)$\\[/tex]
[tex]\textup{Using the Mid point formula we get:}\\$(12,4) = \frac{0 + x_2}{2} + \frac{-1 + y_2}{2} $\\$ \implies x_2 = 24$ \hspace{5mm}\& \hspace{5mm}$y_2 = 9$\\Now the end points of the line segment are:\\$(x_1,y_1) = (0,-1) \hspace{5mm} \& \hspace{5mm} (x_2,y_2) = (24,9)$\\[/tex]
[tex]\textbf{The length of a line segment is given by:}\\$d = \sqrt{{(x_2 - x_1)}^2 + {{(y_2 - y_1)}^2}}$$\therefore d = \sqrt{{(24 - 0)}^2 + {(9 - (-1))}^2}$\\$\implies d = \sqrt{676} = 26$ units.[/tex]
