rWhat are the coordinates of P', the image of P(-1,4) after a reflection in the line x=2?

Question

How do you do a reflection in line X=2? How do you solve this problem? Please explain it to me. Thanks.

Answer 1

As the reflection line is only expressed in x and not y, the y value doesn't change.

The x value of the answer is the distance from the reflection line, but the other way.

2 - -1 = 3
2 + 3 = 5

P'(5, 4)

Answer 2

The line x = 2 is a vertical line drawn 2 units from the origin (0,0)
If the point P(-1,4) is reflected about this line, the horizontal distance of P from this line is : 2 - (-1) = 3. Therefore, the image of P on the other side of line x = 2 will be 3 units horizontally from this line. The x-coordinate of P` will therefore be 2+3 = 5
The y-coordinate will be the same as for P, i.e. 4
The full coordinates are P`(5,4)

Answer 3

The image will be the same distance "behind" the reflection line as the point is "in front" of the line.
2 - (-1) = 2 + 1 = 3, so the point is 3 units "in front" of the line.
2 + 3 = 5 gives the x coordinate of the reflection.
The y value is unchanged by this reflection because the line x = 2 is parallel to the y axis, so the reflection point is P'(5,4)

Answer 4

The distance between the line and the point=2-(-1)=3
rhe coordinates of P' are (5,4)

Answer 5

hmmm.... P(1,-2) is reflected thru x=3 gives: Ans: P'(5,-2) Viola!

Answer 6

P'=(5,4)