Solve the problem. If necessary, round to the nearest tenth.
-Find all ordered pairs on the y-axis of a Cartesian coordinate system that are 10 units from the point (6, 0)
A) (64, 0)
B) (0, -8), (0, 8)
C) (0, 8)
D) (0, -64), (0, 64)

Question

Quizplus · Accepted Answer

The distance formula is used to find the distance between two points in a Cartesian coordinate system, which is $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. For a point on the y-axis, the x-coordinate is 0. So, using the point (6, 0) and a point on the y-axis (0, y), and setting the distance to 10 units, we get $\sqrt{(0 - 6)^2 + (y - 0)^2} = 10$. Simplifying, we find $y = \pm8$, leading to the points (0, -8) and (0, 8).

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