Question

Transformations and Congruence Online Practice
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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

10
10 - no response given

3
3 - incorrect

5

Answer 1

To find the distance between the original point A and its reflected point A 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, the x-coordinate remains the same, but the y-coordinate changes sign. Therefore, the reflected point A would have coordinates (3, -5).

Next, we can use the distance formula to find the distance between the two points A(3, 5) and A'(3, -5). The distance formula is:

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

Plugging in our points:

- \(x_1 = 3\), \(y_1 = 5\)
- \(x_2 = 3\), \(y_2 = -5\)

Now, substituting these values into the formula:

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

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