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 (X=4,Y=4, X=5, Y=5) and the coordinates of C′ are(5,2/6,2/7,2/12,2) .

Answer 1

X=5 C coordinates are (6,2)

Answer 2

Answer:

Line of reflection : x=5

Coordinates of C′ : (6,2)

Step-by-step explanation:

Consider the below figure attached with this question.

From the below figure it is clear that the vertices of polygon ABCD are A(1,6), B(3,5), C(4,2) and D(1,2).

The vertices of image are A'(9,6), B'(7,5) and D'(9,2).

The preimage and image of point A are A(1,6) and A'(9,6) respectively. Here, the y-coordinate is same it means the figure ABCD reflected across a vertical line which is passes through the midpoint of A(1,6) and A'(9,6).

$x=\dfrac{x_1+x_2}{2}$

$x=\dfrac{1+9}{2}$

$x=\dfrac{10}{2}$

$x=5$

Therefore, the line of reflection is x=5.

Since the figure is reflected across x=5, so the rule of reflection is

$(x,y)\rightarrow (2(5)-x,y)$

$(x,y)\rightarrow (10-x,y)$

The coordinates of point C are (4,2).

$C(4,2)\rightarrow C'(10-(4),1)=C'(6,2)$

Therefore, the coordinates of C′ are (6,2).