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Kelsey's neighborhood has a straight road with stop signs at both ends and a fire hydrant at its midpoint. On a map, the fire hydrant is located at (12, 7) and one of the stop signs is located at (3, 11). Where on the map is the other stop sign located?

A. [tex]\(\left(\frac{9}{2}, 2\right)\)[/tex]
B. [tex]\(\left(\frac{15}{2}, 9\right)\)[/tex]
C. (21, 3)
D. (-6, 15)



Answer :

GinnyAnswer
To determine the coordinates of the other stop sign, we need to use the information given:

- The coordinates of the fire hydrant are (12, 7).
- The coordinates of one stop sign are (3, 11).

The problem specifies that the fire hydrant is at the midpoint of the straight road between the two stop signs. To find the coordinates of the other stop sign, we use the midpoint formula:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Here, [tex]\((x_1, y_1)\)[/tex] are the coordinates of the first stop sign, and [tex]\((x_2, y_2)\)[/tex] are the coordinates of the second stop sign. The midpoint of these coordinates is the fire hydrant [tex]\((12, 7)\)[/tex].

We can set up two equations, one for the x-coordinates and one for the y-coordinates:

1. For the x-coordinates:
[tex]\[ \frac{3 + x_2}{2} = 12 \][/tex]
Solving for [tex]\(x_2\)[/tex]:
[tex]\[ 3 + x_2 = 24 \][/tex]
[tex]\[ x_2 = 21 \][/tex]

2. For the y-coordinates:
[tex]\[ \frac{11 + y_2}{2} = 7 \][/tex]
Solving for [tex]\(y_2\)[/tex]:
[tex]\[ 11 + y_2 = 14 \][/tex]
[tex]\[ y_2 = 3 \][/tex]

Thus, the coordinates of the other stop sign are [tex]\((21, 3)\)[/tex].

Therefore, the correct answer is:

C. [tex]\((21, 3)\)[/tex]

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