Question

a. describe the sequence of translations used to move figure 1 onto figure 2. b. determine the coordinates of the image of figure 1 if it is translated 1 unit horizontally and - 8 units vertically. c. explain how you determined the coordinates in part (b). d. verify your answer to part (b) by graphing the image. label it figure 3.

Explanation:

Step1: Identify translation rules

Translation 1: 3 units down and 10 units to the left. Translation 2: 1 unit horizontally and - 8 units vertically (which means 1 unit right and 8 units down).

Step2: For part (a)

The sequence of translations is first move 3 units down and 10 units to the left, then 1 unit right and 8 units down.

Step3: For part (b)

Let the original coordinates of a point in Figure 1 be \((x,y)\). After the first translation (3 units down and 10 units left), the new - coordinates are \((x - 10,y - 3)\). After the second translation (1 unit right and 8 units down), the final coordinates of the image are \((x-10 + 1,y - 3-8)=(x - 9,y - 11)\).

Step4: For part (c)

We determined the coordinates by applying the rules of horizontal and vertical translations. For horizontal movement, we add or subtract from the \(x\) - coordinate (right is positive, left is negative), and for vertical movement, we add or subtract from the \(y\) - coordinate (up is positive, down is negative).

Step5: For part (d)

Graph Figure 1. Apply the first translation (3 units down and 10 units left) to get an intermediate figure. Then apply the second translation (1 unit right and 8 units down) to the intermediate figure to get Figure 3. Check if the coordinates calculated in part (b) match the graphed points.

Answer:

a. First, translate Figure 1 3 units down and 10 units to the left, then translate the resulting figure 1 unit right and 8 units down to get Figure 2.
b. If the original coordinates of a point in Figure 1 are \((x,y)\), the coordinates of its image are \((x - 9,y - 11)\).
c. Used rules of horizontal and vertical translations to calculate coordinates.
d. Graph Figure 1, apply translations step - by - step and check if calculated coordinates match graphed points.