Point P is located in the first quadrant of a coordinate plane. If P is reflected across the x-axis to form P. choose the four s

Question

2 years ago

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Point P is located in the first quadrant of a coordinate plane. If P is reflected across the x-axis to form P. choose the four s

tatements that will always be true
Line segment PP'is parallel to the x-axis.
Line segment Pp'is parallel to the y-axis.
Line segment PP'is perpendicular to the x-axis.
Line segment PP is perpendicular to the y-axis.
The distance from P to the x-axis is equal to the distance from P'to the x-axis.
The distance from P to the y-axis is equal to the distance from P'to the y-axis.

Mathematics

2 answers:

mariarad [96] · Answer 1 · 2023-11-23T05:16:33+03:00

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: $(x,y)\rightarrow (x,-y)$

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.