Question

1. use the figures shown to complete parts (a) through (d). 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).

Explanation:

Step1: Observe figure positions

By comparing the positions of Figure 1 and Figure 2 on the coordinate - grid, we can see the translation.

Step2: Determine horizontal and vertical changes

Count the number of units moved horizontally and vertically. Figure 1 is moved 1 unit to the right (positive x - direction) and 8 units down (negative y - direction).

Step3: Use translation rule for coordinates

If a point $(x,y)$ in Figure 1 is translated 1 unit horizontally and - 8 units vertically, the new coordinates $(x',y')$ of the image point are given by the rule $x'=x + 1$ and $y'=y-8$.

Answer:

a. Figure 1 is translated 1 unit horizontally to the right and 8 units vertically down to move onto Figure 2.
b. Let the coordinates of a point in Figure 1 be $(x,y)$. The coordinates of the corresponding point in the image (after translation) are $(x + 1,y - 8)$.
c. We determined the coordinates in part (b) by using the translation rule. For a horizontal translation of $h$ units and vertical translation of $k$ units, the new coordinates $(x',y')$ of a point $(x,y)$ are given by $x'=x + h$ and $y'=y + k$. Here, $h = 1$ and $k=-8$.