Answer:
Line segment PP'is parallel to the y-axis.
Line segment PP'is perpendicular to the x-axis.
The distance from P to the x-axis is equal to the distance from P'to the x-axis.
Step-by-step explanation:
Given:
Point P is in 1st quadrant and P' is its reflection across x axis.
The figure for the given scenario is given below.
From the figure, following points are clear:
1. Line segment PP' is parallel to y axis (Vertical axis).
2. Line segment PP' is perpendicular to x axis (Horizontal axis).
Now, when we reflect a point across the x axis, the co-ordinate rule states that: [tex](x,y)\rightarrow (x,-y)[/tex]
So, the value of y changes sign. So, vertical distance of the original point is same as that of the reflected point. The only difference is one is above x axis and the other below x axis.
Therefore, the distance from P to the x-axis is equal to the distance from P'to the x-axis.
So, the statements that are true are as follows:
Line segment PP'is parallel to the y-axis.
Line segment PP'is perpendicular to the x-axis.
The distance from P to the x-axis is equal to the distance from P' to the x-axis.
When a point is reflected, it must be reflected across a line.
Options (b), (c), (e) and (f) are true for the reflection.
From the question, we understand that point P is in the first quadrant.
A reflection across the x-axis, will position point P' in the fourth quadrant (see attachment for illustration of the reflection).
From the attached image, we have the following highlights.
The above highlights mean that, options (b), (c), (e) and (f) are true for the reflection.
Read more about reflections at:
https://brainly.com/question/938117
