Question

Pentagon PQRST and its reflection, pentagon P'Q'R'S'T', are shown in the coordinate plane below:

What is the line of reflection between pentagons PQRST and P'Q'R'S'T'?
A)y = x 
B)y = 0 
C)x = 1  
D)x = 0

Answer 1

To get from pentagon PQRST to P'Q'R'S'T' by a reflection of
A) y = x

Answer 2

Option A y = x

Explanation:

In the given figure Pentagon PQRST and its reflection Pentagon P'Q'R'S'T' have been shown.

Pentagon P'Q'R'S'T' have been reflected by a line that passes through origin (0,0) and is perpendicular to the line joining points S(-2,1) and S'(1,-2)

Let the line is y = mx + c

Since line passing through s and s' and slope =
`((y-y')/(x-x') )` =
`(-2-1)/(1+2)=(-3)/(3)` = -1

So line perpendicular to SS' will be

m × (-1) = (-1)

m = 1

The given line will be y = x + c

Since this line passes through (0,0) origin so 'C' will be zero.

Now we can say equation of the line is y = x by which Pentagon PQRST has been reflected.