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

3
3

5
5

10
10

6

Answer 1

When a point is reflected across the x-axis, the x-coordinate remains the same while the y-coordinate changes sign.

For point A with coordinates (3, 5):
- The reflected point A' across the x-axis will have coordinates (3, -5).

To find the distance between the original point A (3, 5) and the reflected point A' (3, -5), we use the distance formula:

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

Substituting in the coordinates of the two points:
- \( (x_1, y_1) = (3, 5) \)
- \( (x_2, y_2) = (3, -5) \)

The calculation becomes:

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

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