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Point B has coordinates (5,2). The x-coordinate of point A is –7. The distance between point A and point B is 15 units. What are the possible coordinates of point A?
The possible coordinates of point A are __.
(Type an ordered pair. Use a comma to separate answers as needed.)
To find the possible coordinates of point A, we can use the distance formula. The distance (d) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by:
[
d = sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
]
In this case, point B has coordinates ((5, 2)), the x-coordinate of point A is (-7), so let the y-coordinate of point A be (y_A). The distance between points A and B is given as 15 units.
Plugging the coordinates into the distance formula, we have:
[
15 = sqrt{(5 – (-7))^2 + (2 – y_A)^2}
]
This simplifies to:
[
15 = sqrt{(5 + 7)^2 + (2 – y_A)^2}
]
[
15 = sqrt{12^2 + (2 – y_A)^2}
]
[
15 = sqrt{144 + (2 – y_A)^2}
]
Now, squaring both sides to eliminate the square root:
[
225 = 144 + (2 – y_A)^2
]
Subtract 144 from both sides:
[
81 = (2 – y_A)^2
]
Taking the square root