Question

The coordinates of the vertices of △JKL are J(3, 4), K(3, 1), and L(1, 1). The coordinates of the vertices of △J′K′L′ are J′(−3,−5), K′(−3,−2), and L′(−1,−2). Drag and drop the answers into the boxes to correctly complete the statement.

A sequence of transformations that maps △JKL to △J′K′L′ is a ---------------------------- followed by a ----------------------------------

a. Translation, Reflection
b. Rotation, Translation
c. Reflection, Rotation
d. Translation, Dilation

Answer 1

A reflection over the y-axis and a translation downward and to the left map △JKL to △J′K′L′. The correct sequence is a reflection followed by a translation.

Step-by-step explanation:

To determine the sequence of transformations that map △JKL to △J′K′L′, we must compare the coordinates of corresponding vertices. We notice that the x-coordinates of J, K, and L (3, 3, and 1) become -3, -3, and -1 respectively in J′, K′, and L′; and the y-coordinates 4, 1, and 1 become -5, -2, and -2 respectively. This indicates that a reflection over the y-axis has occurred, as the signs of the x-coordinates have changed, but not over the x-axis, since the signs of all y-coordinates have also changed. Additionally, the points have moved horizontally and vertically, suggesting a translation.

A suitable reflection to consider is over the y-axis (changing the sign of the x-coordinate), with an additional translation to account for the shifting in both x and y directions. This translation is horizontally to the left (as the x values have become more negative) and vertically downward in the coordinate system (since the y values have become more negative).

The correct sequence of transformations is, therefore, a reflection followed by a translation, corresponding to choice (a) Translation, Reflection from the provided options.