Question

Find all the points having a y-coordinate of -6 whose distance from the point (1,2) is 17.

A. By using the Pythagorean theorem
B. By using the distance formula
C. Both A and B
D. Neither A nor B

Answer 1

To find points with a y-coordinate of -6 and a distance of 17 from the point (1, 2), both the Pythagorean theorem and the distance formula must be used.

Step-by-step explanation:

To find all the points having a y-coordinate of -6 whose distance from the point (1,2) is 17, we can use the distance formula.

1. Let's assume the x-coordinate of the point is x. According to the distance formula, the distance between two points is given by √((x - 1)^2 + (-6 - 2)^2).
2. Simplifying this equation, we get √((x - 1)^2 + 64).
3. To find the x-coordinate, we can solve the equation (x - 1)^2 + 64 = 17^2.
4. By solving this equation, we will obtain two values for x.
5. Substituting these values back into the original equation, we can find the corresponding y-coordinates.
6. These two points will satisfy the given condition.
7. Therefore, the answer is option C, both A and B, as we used both the Pythagorean theorem and the distance formula in the process of finding the points.