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505-555 Level|   Coordinate Geometry|                        
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CEdward
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In the rectangular coordinate system shown above, points O, P, and Q r 16 Apr 2021, 19:47
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This is how I did it.

Let point be (x,y)

Distance formula...

(0 - x)^2 + (0 - y)^2 = (0 - x)^2 + (6 - y)^2
x^2 + y^2 = x^2 + 36 - 12 + y^2
y = 3

So choice is B or E.

Use the same distance formula to see whether (1,3) is equi-distant from each point. It's not.

E.
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Natansha
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In the rectangular coordinate system shown above, points O, P, and Q r 18 Mar 2025, 15:08
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ScottTargetTestPrep
AbdurRakib


In the rectangular coordinate system shown above, points O, P, and Q represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?

A. (3,1)
B. (1,3)
C. (3,2)
D. (2,2)
E. (2,3)

OG Q 2017(Book Question: 24)


Solution:

By looking at the graph, the easiest way is to take the midpoint of PQ (since it is already equidistant to P and Q) as the locations of the fire station. Let it be F. So F = ((0 + 4)/2, (6 + 0)/2) = (2, 3). We see that this point is also equidistant from O = (0, 0). Therefore, (2, 3) must be the location where the fire station should be built.

Alternate Solution:

Recall that the set of points equidistant from two given points is a line that passes through the midpoint of the two given points and that is perpendicular to the line passing through the two points.

Using this fact, we see that every point on the line y = 3 is equidistant to P and O (since the midpoint of P and O is (0, 3)), and every point on the line x = 2 is equidistant to O and Q (since the midpoint of O and Q is (2, 0)). The intersection of the lines y = 3 and x = 2 is the point (2, 3), and this point is equidistant to P, O and Q.

Answer: E
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Hi Scott, how do we come to this conclusion in the highlighted part?
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