Question

The length of a segment withe the given endpoint X(0, -1) and

midpoint M(12, 4).

Answer 1

`\textbf{The length of the line segment is $26$ units.}\\`

Explanation:

`\textup{Given one endpoint and the midpoint of the line segment.}\\The mid point formula is: $$ M = \left( (x_1 + x_2)/(2) \right ) + \left ( (y_1 + y_2)/(2) \right )  $$ \\Now call $(x_1,y_1) = (0,-1)$\& $M = (12,4)$\\`

`\textup{Using the Mid point formula we get:}\\$$(12,4) = (0 + x_2)/(2) + (-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)$\\`

`\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 = √(676) = 26$ units.`