Question

match figures 1,2,3, 4 above with the correct translation rule using the dropdown box.
figure 1
figure 2
figure 3
figure 4

Explanation:

Step1: Analyze Figure 1

To find the translation, pick a point on the original figure and its corresponding point on the translated figure. Let's assume a point $(x,y)$ on the original triangle in Figure 1. If we observe carefully, moving from a point on the left - hand triangle to the corresponding point on the right - hand triangle, we see that we move 6 units to the right (increase in x - value) and 4 units down (decrease in y - value). The translation rule is $(x,y)\to(x + 6,y-4)$.

Step2: Analyze Figure 2

Pick a point on the original trapezoid ABCD. Comparing it to the translated trapezoid $A'B'C'D'$, we note that we move 4 units to the right (increase in x - value) and 3 units down (decrease in y - value). The translation rule is $(x,y)\to(x + 4,y-3)$.

Step3: Analyze Figure 3

For the triangle in Figure 3, by observing a point on the original triangle PQR and its corresponding point on the translated triangle $P'Q'R'$, we move 4 units to the right (increase in x - value) and 3 units down (decrease in y - value). The translation rule is $(x,y)\to(x + 4,y-3)$.

Step4: Analyze Figure 4

Looking at a point on the original triangle in Figure 4 and its corresponding point on the translated triangle, we move 5 units to the left (decrease in x - value) and 3 units up (increase in y - value). The translation rule is $(x,y)\to(x - 5,y+3)$.

Answer:

FIGURE 1: $(x,y)\to(x + 6,y-4)$
FIGURE 2: $(x,y)\to(x + 4,y-3)$
FIGURE 3: $(x,y)\to(x + 4,y-3)$
FIGURE 4: $(x,y)\to(x - 5,y+3)$