Solve the problem.
-Find all the points having an x-coordinate of 9 whose distance from the point (3, -2)is 10.
A)(9, 6), (9, -10)
B)(9, 2), (9, -4)
C)(9, -12), (9, 8)
D)(9, 13), (9, -7)

Question

Quizplus · Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. Here, we're given one point $(3, -2)$ and a distance of 10, with the x-coordinate of the other point being 9. Plugging these into the distance formula, we get $\sqrt{(9-3)^2 + (y-(-2))^2} = 10$. Simplifying, $\sqrt{36 + (y+2)^2} = 10$. Squaring both sides gives $36 + (y+2)^2 = 100$, leading to $(y+2)^2 = 64$. Solving for $y$, we find $y+2 = 8$ or $y+2 = -8$, giving $y = 6$ or $y = -10$. Therefore, the points are $(9, 6)$ and $(9, -10)$.

Solve the Problem. -Find All the Points Having an X-Coordinate of 9 Whose