Question

In the diagram, polygon ABCD is flipped over a line of reflection to form a polygon with its vertices at A′, B′, C′, and D′. Points A′, B′, and D′ are shown, but the line of reflection and point C′ are not. The line of reflection is ? , and the coordinates of C' are (6,2). What is the line of reflection?

Answer 1

Answer: The line of reflection must be x=5.

Step-by-step explanation:

Given: In the diagram, polygon ABCD is flipped over a line of reflection to form a polygon with its vertices at A′, B′, C′, and D′. Points A′, B′, and D′ are shown, but the line of reflection and point C′ are not .

coordinates of C from the graph = (4,2)

If the coordinates of C'=(6,2)

we can see that value of y isn't change with reflection therefore the line of reflection would be x= ordinate of C'+ ordinate of C divided by 2=6+4 divided by 2=10 divided by 2=5

Therefore, the line of reflection must be x=5.

Answer 2

In order to find line of reflection, we can calculate mid-line of most touching coordinates which is C & C'

Here, C = (4, 2) & C' = (6, 2)

We can easily see, the reflection here is across y-axis on x-axis, 
so it would be: 4 + 6 / 2 = 10/2 = 5

In short, Your Answer would be: 5th line of x-axis

Hope this helps!