Answer:
C. [tex] x = -2 [/tex]
Step-by-step explanation:
A rectangle has two lines of symmetry. That is, the line that divides the rectangle into two equal halves.
Taking a look at the rectangle that is placed on the coordinate grid. At what points do you think the two lines of symmetry can be located at that will give us two possible equal halves?
One will be horizontal, the other will be vertical.
For the horizontal line, the line of symmetry can be located at y = 5. If an horizontal line cuts through the rectangle at y = 5, we would have two equal halves.
Thus, an equation for a horizontal line is often represented as [tex] y = k [/tex]. Where k is a constant, because every coordinate point on the horizontal line would have the same value of k, which is where the line cuts across the y-axis. The slope of am horizontal line remains zero also.
Therefore, the equation of the line of symmetry of the rectangle shown in the coordinate grid would be:
✅[tex] y = 5 [/tex]
The second line of symmetry which is vertical, would cut across the rectangle at x = -2.
Thus, the slope of a vertical line is undefined.
The equation of a vertical line is represented as x = h.
Where h is a constant, since all coordinates along the vertical line would surely have a x-coordinate value of -2, regardless of what y-coordinate value they have.
Therefore, h, in this case is -2.
Thus, the equation that represents the second line of symmetry of the rectangle above would be:
✅[tex] x = -2 [/tex].
The two equations that represent the two lines of symmetry of the rectangle, respectively, are:
[tex] y = 5 [/tex]
[tex] x = -2 [/tex]
From the options given, the only correct option provided is:
[tex] x = -2 [/tex].
