Question

Which unique sequence of rigid motions maps quadrilateral ABCD to quadrilateral EFGH?

6
5
A
IB
x
634
1 2 3 4 5 6
E
G
A
A reflection over the x-axis followed by a translation of (z,y) → (2, y - 4).
B. A reflection over the y-axis followed by a translation of (1,y) → (I, y-6).
C. A translation of (I, y) + (1, y-3) followed by a reflection over the y-axis.
A translation of (€,y) → (3-6, y) followed by a reflection over the x-axis.

Answer 1

The unique sequence of rigid motions that maps quadrilateral ABCD to EFGH are;

B. A reflection over the y-axis followed by a translation of (I, y) → (I, y - 6)

('I' is the image of 'x' after reflection)

Explanation:

The coordinates of the vertices of the quadrilateral ABCD are;

A(-5, 4), B(-2, 4), C(-2, 1), and D(-5, 2)

The coordinates of the vertices of the quadrilateral EFGH are;

E(5, -2), F(2, -2), G(2, -5), and H(5, -4)

By analysis, we have;

The signs of the x-coordinate of the preimage and the image are opposite, therefore, one of the rigid motions is a reflection across the y-axis

Similarly, the common difference between the y-coordinate values of the image and the preimage are;

-2 - 4 = -6

-2 - 4 = -6

-5 - 1 = -6

-4 - 2 = -6

The common difference between the y-coordinates of the image and the preimage is -6, therefore, the y-values are obtained by a translation of y - 6 units

Therefore, the unique sequence of rigid motions that maps quadrilateral ABCD to EFGH are a reflection over the y-axis followed by a translation of (I, y) → (I, y - 6).