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.