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

Question

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

(1 point)

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.

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.*******

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.

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

The unknown point could be anywhere on a circle of radius 14 and center (0,7)

Answer 2

Let the unknown point be (x,y) , the other point is (0,7) and they are 14 units apart.
then (x-0)^2 + (y-7)^2 = 14^2
x^2 + (y-7)^2 = 196 <---- a circle with centre (0,7) and radius 14

There is an infinite number of such points
as long as -14 ≤ x ≤ 14, and -7 ≤ y ≤ 21

x^2 = 196 - (y-7)^2
x = ± √(196 - (y-7)^2)
sub in any value of y within the range I stated.
e.g. y = 5
x = ±√(196-4) = ±√192 = ±64√3 <---- two points: (64√3,5) and (-64√3,5)
e.g. y = 3
x = ± √(196 - 16) = ±√180 = ±6√5 <-- two more points (6√5, 3) and (-6√5,3)
notice that the given point (0,21) also works, but is only one of the infinite number of points.

Answer 3

Thank you. So the answer is (0,21)?

Answer 4

I guess you didn't read my post, I said:
There is an infinite number of such points
(0,21) is just one of them, so it (14,7), (-14,7) and (0,-7) and billions and billions more