In order to score well in the exams, one must understand the concepts in maths. That is possible with us here we provide quick and easy learning tricks in reflection here. Reflection of a Point in a Line Parallel to the y-axis is a scoring topic from the chapter reflection. Scroll down this page to know what is meant by Reflection of a Point in a Line Parallel to the y-axis with suitable examples. Step by step explanation is given for the problems by the math experts.
Also Refer:
- Reflection of a Point in a Line Parallel to the x-axis
- Reflection of a Point in the y-axis
- Reflection of a Point in the x-axis
What is the Reflection of a Point in a Line Parallel to the y-axis?
Let P be the point on the x-axis with the coordinates (x, y). Let the image of P be P’ in the horizontal line drawn on the y-axis. The image of the point (x, y) in the line parallel to the y-axis. When it comes to the refection of a point in a line parallel to the y-axis the sign of the y-axis will be changed and the sign of the x-axis remains the same.
Reflection of a Point in a Line Parallel to the y-axis Examples
Example 1.
The point P ( -4, -7) on reflection in the y-axis is mapped on P’. The point P’ on reflection in the origin is mapped on P”. Find the coordinates of P’ and P”. Write down a single transformation that maps P onto P”.
Solution:
Given that the point P (-4, -7)
And, P’ is the image of point P in the y-axis
The coordinates of P’ will be (4, -7)
Again,
P” is the image of P’ under reflection in origin.
Thus, the coordinates of P” will be (-4, 7).
The single transformation that maps P onto P” is the x-axis.
Example 2.
Point A(5, 7) is first reflected in the origin to point A’. Point A’ is then reflected in the y-axis to point A”.find the coordinates of A”.
Solution:
Given that the point is A(5,7)
Coordinates of A’ after reflection from origin =(-5,-7)
And after reflection from y-axis coordinates becomes =A”=(5,-7)
Example 3.
A point P (a, b) is reflected in the x-axis to P’ (4, 3). Write down the values of a and b. P” is the image of P, reflected in the y-axis. Write down the coordinates of P”. Find the coordinates of P”, when P is reflected in the line, parallel to the y-axis, such that x = 4.
Solution:
The coordinates of the point P be(4,-3)
Hence the value of a and b are
4 and -3
after reflection coordinates of P”=(-4,3)
Coordinates of p after reflection from x=4 are (8,-3)
Example 4.
The reflection of point (-7, -9) through the y-axis is.
Solution:
When reflected through the y axis, the coordinates x value reverses its sign
This means the positive becomes negative, and the negative becomes positive.
Now we have, the coordinates (-7, -9) its reflection through the y-axis gives us (-7, 9).
Example 5.
The reflection of point (-3, -5) through the y-axis is.
Solution:
When reflected through the y axis, the coordinates x value reverses its sign
This means the positive becomes negative, and the negative becomes positive.
Now we have, the coordinates (-3, -5) its reflection through the y-axis gives us (-3, 5).
FAQs on Reflection of a Point in a Line Parallel to the y-axis
1. When a line is parallel to the Y-axis What is the slope?
The slope of the line parallel to the y-axis is undefined.
The line parallel to the y axis is at an angle of 90º to the x-axis
Then the slope of this line is tan90º, which is undefined.
2. How do you find the slope of the y-axis?
The slope-intercept form of a line is: y=mx+b
where m is the slope and
b is the y-intercept.
3. When a line is parallel to the y-axis?
A line is parallel to the x-axis and y-axis either the x-coordinate or y-coordinate is fixed or constant throughout the line and the line passes from either (0, a) or (a, 0).