Answer:
The possible coordinates of point A are (-3, 8) and (-3, -4).
Explanation:
We can find the possible coordinates of point A by using the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is equal to the square root of (x2-x1)^2 + (y2-y1)^2. We know that the x-coordinate of point A is -3 and the distance between point A and point B is 10 units. We can use this information to solve for the y-coordinate of point A:
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d = sqrt((x2-x1)^2 + (y2-y1)^2)
d = sqrt((5-(-3))^2 + (2-y1)^2)
d = sqrt(8^2 + (2-y1)^2)
d = sqrt(64 + (2-y1)^2)
d = sqrt(64 + (y1-2)^2)
d = 10
sqrt(64 + (y1-2)^2) = 10
64 + (y1-2)^2 = 100
(y1-2)^2 = 36
y1-2 = +/- 6
y1 = 8 or -4
Therefore, the possible coordinates of point A are (-3, 8) and (-3, -4).