Question

Point A is on figure B and is reflected across the x -axis. If point has coordinates of (3,5) , what is the distance between the original point A and the reflected point A?(1 point) Responses 6 6 - no response given 3 3 - incorrect 10 10 - no response given 5 5 - no response given Incorrect

Answer 1

To find the reflected coordinates of point A (3, 5) across the x-axis, we change the sign of the y-coordinate.

The reflection of point A (3, 5) across the x-axis is (3, -5).

Now we can calculate the distance between the original point A (3, 5) and the reflected point A (3, -5). The distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in the coordinate plane can be found using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Substituting the coordinates of the two points:

\[
d = \sqrt{(3 - 3)^2 + (-5 - 5)^2} = \sqrt{0^2 + (-10)^2} = \sqrt{100} = 10
\]

Therefore, the distance between the original point A and the reflected point A is 10.