Answer: The required transformation from ABCDE to MNOPQ is the reflection across the y axis.
And, the co-ordinates of the vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3) and Z(3, 1).
Step-by-step explanation: Given that a polygon ABCDE has the vertices A(2, 8), B(4, 12), C(10, 12), D(8, 8), and E(6, 6). Polygon MNOPQ has the vertices M(-2, 8), N(-4, 12), O(-10, 12), P(-8, 8), and Q(-6, 6).
A transformation or sequence of transformations that can be performed on polygon ABCDE to show that it is congruent to polygon MNOPQ.
We are to find the transformation.
We note that if (x, y) denotes the co-ordinates of a vertex of polygon ABCDE, then the corresponding vertex of polygon MNOPQ has co-ordinates (-x, y).
So, the sign before the x co-ordinate is changing, which gives the reflection across the y axis.
Therefore, the required transformation is the reflection across the y axis.
Also, the polygon is translated 3 units right and 5 units down so that it will coincide with a congruent polygon VWXYZ.
We are to find the co-ordinates of the vertices of polygon VWXYZ.
According to the given transformation rule, the co-ordinates of polygon MNOPQ changes as follows :
(x, y) ⇒ (x+3, y-5).
So, the vertices of polygon VWXYZ are
V(-2+3, 8-5) = V(1, 3),
W(-4+3, 12-5) = W(-1, 7),
X(-10+3, 12-5) = X(-7, 7),
Y(-8+3, 8-5) = Y(-5, 3),
Z(-6+3, 6-5) = Z(-3, 1).
Thus, the co-ordinates of the vertices of polygon VWXYZ are V(1, 3), W(-1, 7), X(-7, 7), Y(-5, 3) and Z(3, 1).