Question

Rectangle J′K′L′M′ shown on the grid is the image of rectangle JKLM after transformation. The same transformation will be applied on trapezoid STUV.

Rectangle JKLM is drawn on the grid with vertices J at negative 7, negative 6. K is at negative 4, negative 6. L is at negative 4, negative 2. M is at negative 7, negative 2. Rectangle J prime K prime L prime M prime is drawn with vertices J at prime 6, negative 9. K prime is at 9, negative 9. L prime 9, negative 5. M prime is at 6, negative 5. Trapezoid STUV is drawn with vertices at S 3, 2. T is at 5, 5. U is at 2, 6. V is at 1, 4.

What will be the location of T′ in the image trapezoid S′T′U′V′?

(18, −2)
(18, 2)
(15, −2)
(15, 2)

Answer 1

The transformed figure has the opposite orientation (A'B'C'D' is counterclockwise, whereas ABCD is clockwise), so a reflection is involved. The segment C'D' is still at the bottom, as is CD, so the reflection must be across a vertical line.

In the attached, the light-blue figure A''B''C''D'' shows the reflection of ABCD across the y-axis. It is easy to see that figure A'B'C'D' is a translation of that 5 units downward.

The appropriate choice is the 2nd one ...

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