Answer:
The answer is (C) (-2,0).
Explanation:
To determine which coordinate is not 5 units away from the point (1, 4), we need to calculate the distance between (1, 4) and each of the given points using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
where (x1, y1) is the point (1, 4) and (x2, y2) is the coordinate we are testing.
Starting with option A, which is (4, 0):
d = sqrt((4 - 1)^2 + (0 - 4)^2) = sqrt(9 + 16) = 5
Option A is 5 units away from (1, 4), so it could be the correct answer.
Moving on to option B, which is (-4, 0):
d = sqrt((-4 - 1)^2 + (0 - 4)^2) = sqrt(25 + 16) = sqrt(41)
Option B is not 5 units away from (1, 4), so it could be the correct answer.
Moving on to option C, which is (-2, 0):
d = sqrt((-2 - 1)^2 + (0 - 4)^2) = sqrt(9 + 16) = 5
Option C is 5 units away from (1, 4), so it is not the correct answer.
Finally,option D is (1, 9):
d = sqrt((1 - 1)^2 + (9 - 4)^2) = sqrt(25) = 5
Option D is 5 units away from (1, 4), so it is not the correct answer.
Therefore, the coordinate that is not 5 units away from (1, 4) is option C, which is (-2, 0). The answer is (C) (-2,0).