Answer:
32 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Define the two given points:
- Let (x₁, y₁) = (-7, -24)
- Let (x₂, y₂) = (-7, 8)
Substitute the two points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(-7-(-7))^2+(8-(-24))^2}[/tex]
[tex]\implies d=\sqrt{(-7+7)^2+(8+24)^2}[/tex]
[tex]\implies d=\sqrt{(0)^2+(32)^2}[/tex]
[tex]\implies d=\sqrt{32^2}[/tex]
[tex]\implies d=32[/tex]
Note: As the two given points have the same x-coordinate, the line segment (between the points) is a vertical line. Therefore, to find the distance between the two given points, simply calculate the difference between the y-coordinates:
[tex]\implies 8 - (-24) = 8+23=32[/tex]
