DISTANCE
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Find the length of the segment whose endpoints are (-8,-4) and (4,-8).
SOLUTION:
To find the length, we will find the distance between the two endpoints using the formula:
[tex]d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}[/tex]
- [tex]x_1,y_1[/tex] = (-8, -4)
- [tex]x_2, y_2[/tex] = (4, -8)
[tex]\\[/tex]
[tex] \begin{array}{l}\tt d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}} \\ \\ \tt d = \sqrt{ \lbrack 4 - ( - 8) \rbrack ^{2} + \lbrack( - 8) - ( - 4) \rbrack^{2} } \\ \\ \tt d = \sqrt{(4 + 8 {)}^{2} + ( - 8 + 4 {)}^{2} } \\ \\ \tt d = \sqrt{(12 {)}^{2} + ( - 4 {)}^{2} } \\ \\ \tt d = \sqrt{144 + 16} \\ \\ \tt d = \sqrt{160} \\ \\ \boxed{ \red{\tt d = 4 \sqrt{10} }} \end{array}[/tex]
∴ The length of the segment is 4√10.
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