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 - incorrect

3
3 - no response given

10
10 - no response given

5

Answer 1

To find the distance between the original point A and its reflection across the x-axis, we first need to determine the coordinates of the reflected point.

The original point A has coordinates (3, 5). When a point is reflected across the x-axis, its x-coordinate remains the same, while its y-coordinate changes sign.

Therefore, the coordinates of the reflected point A will be (3, -5).

Now, we can calculate the distance between the original point A (3, 5) and the reflected point A (3, -5) using the distance formula:

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

Substituting the coordinates into the formula:

\[
x_1 = 3, \quad y_1 = 5, \quad x_2 = 3, \quad y_2 = -5
\]

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

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