Question

The rule T1, -4 RO, 180°(x, y) is applied to rectangle KLMN. Which rectangle shows the final image??

Answer 1

Figure 3.

Explanation:

We perform the rotation first. A 180° rotation about the origin maps every point

(x, y)→(-x, -y). This means it negates both the x- and y-coordinates.

The pre-image points are:

K(3, -4); L(3, -1); M(5, -1); N(5, -4). Performing the rotation and negating the coordinates will give us:

K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).

Now we perform the translation. The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate. This maps to our new points:

K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)

These are the points of figure 3.

Answer 2

Let me help you!

Looking at the visual, we can see five figures: KLM, 1, 2, 3, and 4.
Applying the rule T1, -4 RO, 180°(x, y) to rectangle KLMN - without even solving - just by merely observing, we can say (without a doubt) that the rectangle KLMN will most likely fall in the negative axis.

First rotation: -4 to the left.
Second rotation: -4 to the left.
Last rotation: -4 to the left making the last figure 3. <----- What we are looking for!

Therefore, the rectangle which shows the final image is figure 3 or rectangle 3.