Question

Line segment CD is shown on a coordinate grid:

The line segment is reflected about the y-axis to form C'D'. Which statement describes C'D'?

A. C'D' is perpendicular to CD.
B. C'D' is half the length of CD.
C. C'D' is greater than twice the length of CD.
D. C'D' and CD are equal in length.
PICTURE BELOW

Answer 1

Answer: The correct option is

(D) C'D' and CD are equal in length.

Step-by-step explanation: We are given that a line segment CD shown on a co-ordinate grid in the graph.

The line segment CD is reflected about the y-axis to form C'D'.

We are to select the statement that describes C'D'.

From the graph, we see that the co-ordinates of the endpoints of line segment CD are C(1, 2) and D(1, -1).

We know that

if a point (x, y) is reflected about the Y-axis, then its co-ordinates changes to (-x, y).

So, after reflection about Y-axis, the co-ordinates of the points C and D changes to

C(1, 2) ⇒ C'(-1, 2),

D(1, -1) ⇒ D'(-1, -1).

Now, the length of CD as calculated using distance formula is

`L_(CD)=√((-1-2)^2+(1-1)^2)=\sqrt9=3~\textup{units},\\\\L_(C'D')=√((-1-2)^2+(-1+1)^2)=√(9)=3~\textup{units}.`

Thus, the lengths of CD and C'D' are equal.

Option (D) is CORRECT.