Question

The vertices of parallelogram CDEF are reflected in the line y = x. Which of the following represents the new coordinates of the vertices after reflection?

a) C(-1, 2), D(1, 7), E(-2, 6), F(-4, 1)
b) C(-1, 2), D(1, 7), E(-2, 6), F(-4, -1)
c) C(2, -1), D(1, 7), E(-2, 6), F(-4, 1)
d) C(2, -1), D(7, 1), E(6, -2), F(1, -4)

Answer 1

After reflecting the vertices of the parallelogram in the line y = x, the new coordinates are C(2, -1), D(7, 1), E(6, -2), F(1, -4), which corresponds to option d.

Step-by-step explanation:

The student is asking about the reflection of the vertices of a parallelogram in the line y = x. When reflecting a point across the line y = x, the x-coordinate and y-coordinate of the point are switched. Therefore, if we have a point (a, b), after reflection, it will be (b, a).

Given the possible coordinate options for vertices C, D, E and F, we need to apply this rule to see which one represents the correct reflection:

1. C(-1, 2) after reflection becomes (2, -1)
2. D(1, 7) after reflection becomes (7, 1)
3. E(-2, 6) after reflection becomes (6, -2)
4. F(-4, 1) after reflection becomes (1, -4)

Therefore, the correct coordinates after reflecting them in the line y = x are C(2, -1), D(7, 1), E(6, -2), F(1, -4), which corresponds to option d.