Chapter 1.3, Problem 76STP

To determine

To calculate the length

Answer to Problem 76STP

Approximate length of $\overline{AB}$ 24.17 units.

Explanation of Solution

Given information:

End points of $\overline{AB}$ is (-3,5)

And mid point is (2,-6)

Formula used:

Distance formula is,

  $d=\sqrt{{(x_2^{}-x_1^{})}^2+{(y_2^{}-y_1^{})}^2}$

Calculation:

For the galf length of the line segment $\overline{AB}$ , substituting the value,

  $half\_length=\sqrt{{\{2-(-3)\}}^2+{(-6-5)}^2}$

On solving,

  $half\_length=\sqrt{25+121}$

On solving,

  $half\_length=\sqrt{146}$

Square rooting,

  $half\_length=12.08$

Since, mid point is the middle point of the given line segment is half the length. Hence, for length of $\overline{AB}$ ,

  $\overline{AB}=12.08\times 2$

On solving,

  $\overline{AB}\approx 24.17$

Hence, approximate length of $\overline{AB}$ 24.17 units.