Pythagorean Theorem

Question

Given the following information, can you find the coordinates of the unknown point? Explain.

Two points are 14 units apart. The first point is located at (0,7).

(1 point)

1. The unknown point is (12, 0). Substituting into the Pythagorean Theorem gives 14^2=a^2+7^2. Solving this for a gives a value of approximately 12.
2. The unknown point cannot be found. When substituting into the distance formula, there will be two unknowns, the x-coordinate and the y-coordinate of the unknown point.
3. The unknown point is (0, 21). Since the first point is located on the y-axis, the second point would be located 14 units away from it, also on the y-axis.
4. The unknown point cannot be found. Neither the distance formula nor the Pythagorean Theorem can be sued to work backwards from a distance to find the coordinates of a point.

Answer 1

Consider (0,7) as the center of a circle with radius 14. The 2nd point can be anywhere on that circle, including (0.21), (0,-7), (-14,7), or (14,7) or any of an infinite number of points on the circle. With another unknown 3rd point you can construct a right angled triangle. More information is needed to find either other side of the triangle