Question

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A land surveyor places two stakes 500 ft apart and locates the midpoint between the stakes. From the midpoint, he needs to place another stake 100 ft away that is equidistant to the two original stakes. To apply the Perpendicular Bisector Theorem, the land surveyor would need to identify a line that is

A .perpendicular to the line connecting the two stakes and going through the midpoint of the two stakes
B .parallel to the line connecting the two stakes and going through the midpoint of the two stakes
C .perpendicular to the line connecting the two stakes and going through one of the two original stakes
D. parallel to the line connecting the two stakes and going through one of the two original stakes

Answers

1. Answer:
Letter A is the answer
Step-by-step explanation:
A perpendicular bisector is a perpendicular line that divides a line into two equal halves
To apply the Perpendicular Bisector Theorem, the land surveyor will need to identify; the midpoint along the line connecting the two stakes
The reason why the surveyor needs to identify the midpoint is as follows:
According to the Perpendicular Bisector Theorem, all points on the perpendicular bisector of a line are of equal distance from the line’s endpoint
In order to apply the perpendicular bisector, the surveyor would need to identify the midpoint from which the third stake can be placed 100 ft. along a perpendicular bisector drawn from the midpoint
Therefore, the surveyor needs to identify; the midpoint along the line connecting the two stakes

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