Question

The vertices of quadrilateral PQRS are P(-4, 2), Q(-1, 1), R(-1, -3), S(-3,-1).

The vertices of quadrilateral ABCD are A(-3, 7), B(0, 6), C(0,2), D(-2, 4) so that
PQRS = ABCD. Which best describes the congruence transformation?
(A) rotation 90° counterclockwise about the origin
(B) reflection in the y-axis
(C) translation along the vector (1,5)
(D) rotation 90° clockwise about the origin

Answer 1

The best description of the congruence transformation between the two given quadrilaterals is a translation along the vector (1,5), which is an option (C).

Step-by-step explanation:

To determine the congruence transformation between the two quadrilaterals, we need to consider how the coordinates of one quadrilateral relate to the other. Looking at the given coordinates of quadrilateral PQRS and quadrilateral ABCD, we notice that each vertex of ABCD is 1 unit to the right and 5 units up compared to the corresponding vertex of PQRS. This indicates that the transformation is a translation, where each point is moved by the same vector. Specifically, the vector is (1,5), which we can write as (x' = x + 1, y' = y + 5).

Thus, the correct transformation that maps quadrilateral PQRS onto ABCD is an option (C) translation along the vector (1,5).

To verify this transformation mathematically, we can add the transformation vector to each vertex in PQRS and see that we obtain the coordinates of the corresponding vertex in ABCD:

• P(-4, 2) + (1, 5) = (-3, 7) = A
• Q(-1, 1) + (1, 5) = (0, 6) = B
• R(-1, -3) + (1, 5) = (0, 2) = C
• S(-3,-1) + (1, 5) = (-2, 4) = D