Question

The distance between two points is √234. One of the points is (6,4). Which could be the other point? Explain your answer.

Option 1: (2, 5)
Option 2: (2, -3)
Option 3: (8, 2)
Option 4: (-2, -5)"

Answer 1

Using the Pythagorean theorem to determine the distance between the given point (6,4) and each of the options, none of the options result in a distance of √234, indicating an error in the options or missing information in the question.

Step-by-step explanation:

To determine which of the provided points could be the other point given that the distance between this point and (6,4) is √234, we can use the Pythagorean theorem which relates the legs of a right triangle to the length of the hypotenuse. Specifically, the distance between two points (x1, y1) and (x2, y2) in a Cartesian coordinate system is √((x2 - x1)2 + (y2 - y1)2).

We apply this formula to each option:

1. (2, 5): √((2 - 6)2 + (5 - 4)2) = √16 + 1 = √17, which does not equal √234.
2. (2, -3): √((2 - 6)2 + (-3 - 4)2) = √16 + 49 = √65, which does not equal √234.
3. (8, 2): √((8 - 6)2 + (2 - 4)2) = √4 + 4 = √8, which does not equal √234.
4. (-2, -5): √((-2 - 6)2 + (-5 - 4)2) = √64 + 81 = √145, which does not equal √234.

None of the options results in a distance of √234 when paired with the point (6,4). Hence, there could be an error in the options provided, or perhaps there are additional constraints or information not included in the question.