Question

Pentagon PQRST and its reflection, pentagon P'Q'R'S'T', are shown in the coordinate plane below: Pentagon PQRST and pentagon P prime Q prime R prime S prime T prime on the coordinate plane with ordered pairs at P negative 4, 6, at Q negative 7, 4, at R negative 6, 1, at S negative 2, 1, at T negative 1, 4, at P prime 6, negative 4, at Q prime 4, negative 7, at R prime 1, negative 6, at S prime 1, negative 2, at T prime 4, negative 1. What is the line of reflection between pentagons PQRST and P'Q'R'S'T'?

Answer 1

line y = x

Explanation:

Reflection across the line y = x, translate the point from (x, y) to (y, x).

Coordinates of the points are:

P (-4, 6)

Q (-7, 4)

R (-6, 1)

S (-2, 1)

T (-1, 4)

P' (6, -4)

Q' (4, -7)

R' (1, -6)

S' (1, -2)

T' (4, -1)

It can be seen that for every point and its translation, i. e., P and P', Q and Q', R and R', S and S', T and T'; the translation (x, y) -> (y, x) was made.

Answer 2

The line of reflection is y=x.

Explanation:

It is given that pentagon PQRST reflected to make the pentagon P'Q'R'S'T'.

The vertices of preimage are P(-4,6), Q(-7,4), R(-6,1), S(-2,1) and T(-1,4).

The vertices of image are P'(6,-4), Q'(4,-7), R'(1,-6), S'(1,-2) and T'(4,-1).

The relation between preimage and image is defined by the rule

`(x,y)\rightarrow (y,x)`

It is the rule of reflection about the line y=x.

Therefore the line of reflection between pentagons PQRST and P'Q'R'S'T' is y=x.