The question is incomplete. Here is the complete question.
Point P is located in the first quadrant of a coordinate plane. If P is reflected across the x-axis to form P', choose four statements that will always be true.
I) Line segment PP' is parallel to the x-axis.
II) Line segment PP' is parallel to the y-axis.
III) Line segment PP' is perpendicular to the x-axis.
IV) Line segment PP' is perpendicular to the y-axis.
V) The distance from P to the x-axis is equal to the distance from P' to the x-axis.
VI) The distance from P to the y-axis is equal to the distance from P' to the y-axis.
II) Line segment PP' is parallel to the y-axis.
III) Line segment PP' is perpendicular to the x-axis.
V) The distance from P to the x-axis is equal to the distance from P' to the x-axis.
VI) The distance from P to the y-axis is equal to the distance from P' to the y-axis.
Step-by-step explanation: Reflection is a type of transformation, which represent a flip of a figure or point, i.e., one is the image of the original.
For example:
Point P is located at the 1st quadrant of the plane, meaning it has positives x- and y-coordinates. When it is reflected across x-axis, point P' "acquires" positive x-coordinate and negative y-coordinate.
As it is a reflection, point P and point P' has the same coordinates, which means, point P' is as distant from x-axis and y-axis as point P.
So, analysing, each statement above:
Statement (I) is false because one point is located at 1st quadrant and the other is at the 4th quadrant, so the line linking both points must be parallel to y-axis; Since (I) and (II) can't be true at the same time, statement (II) is true.
Statements (III) and (IV) can't be true at the same time either. If the line segment is parallel to y-axis, it must form a 90° angle with x-axis, so statement (III) is true.
Statements (V) and (VI) are both true because point P and point P' have the same coordinates and so are equally distant from x-axis and y-axis.
In conclusion, statements (II), (III), (V) and (VI) will always be corrected for a point reflected across the x-axis.
