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)
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.
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.
Thank you. So the answer is (0,21)?
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
To find the coordinates of the unknown point, we can use the Pythagorean Theorem or the distance formula. Let's go through the given information and see which approach we can use.
We are given two points: one at (0,7) and an unknown point. The distance between these two points is 14 units.
Using the Pythagorean Theorem, we can form a right triangle where the line connecting the two points is the hypotenuse. The vertical side of the triangle (y-coordinate) would be the difference between the y-coordinate of the unknown point and the y-coordinate of the given point, which is 7. The horizontal side of the triangle (x-coordinate) would be the difference between the x-coordinate of the unknown point and the x-coordinate of the given point, which is 0.
The Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we have 14^2 = a^2 + 7^2, where a represents the horizontal side (x-coordinate).
By solving this equation, we find that a is equal to approximately 12. Therefore, the x-coordinate of the unknown point is 12.
However, we do not have enough information to determine the y-coordinate of the unknown point. The y-coordinate could be anything as long as the distance between the two points is 14 units.
Therefore, the coordinates of the unknown point are (12, y), where y can be any value.
However, if we know that the first point is located on the y-axis, then the second point would also be located on the y-axis, 14 units away from the first point. In this case, the coordinates of the unknown point would be (0, 21).
In summary, the coordinates of the unknown point cannot be determined without additional information. If the first point is located on the y-axis, then the unknown point would be (0, 21). Otherwise, the y-coordinate of the unknown point remains unknown.