Question

exercises list the ordered pair of the points given. perform the translation using only arithmetic. then, list the ordered pair of the translated points. 1. $t_{(-1,1)}$ e (__, ) → e (, ) b (, ) → b (, ) 2. $t_{(3,2)}$ x (, ) → x (, ) y (, ) → y (, ) 3. $t_{(-3,4)}$ k (, ) → k (, ) h (, ) → h (, ) 4. $t_{(-5,1)}$ u (, ) → u (, ) p (, ) → p (, ) 5. $t_{(-10,-3)}$ b (, ) → b (, ) x (, ) → x (, ) 6. $t_{(-3,3)}$ k (, ) → k (, ) p (, ) → p (, __)

Explanation:

Step1: Recall translation rule

For a translation $T_{(a,b)}$, if a point $(x,y)$ is translated, the new - point $(x',y')$ has coordinates $x'=x + a$ and $y'=y + b$.

Step2: Assume point - coordinates from the graph (let's assume some sample coordinates for illustration purposes).

Let's assume $E(2,3)$, for $T_{(-1,1)}$:
$x_E'=2+( - 1)=1$, $y_E'=3 + 1=4$, so $E'(1,4)$
Let's assume $B(5, - 2)$, for $T_{(-1,1)}$:
$x_B'=5+( - 1)=4$, $y_B'=-2 + 1=-1$, so $B'(4,-1)$
For $T_{(3,2)}$, assume $X(1,1)$
$x_X'=1 + 3=4$, $y_X'=1+2 = 3$, so $X'(4,3)$
Assume $Y(0,0)$
$x_Y'=0 + 3=3$, $y_Y'=0 + 2=2$, so $Y'(3,2)$
For $T_{(-3,4)}$, assume $K(3,1)$
$x_K'=3+( - 3)=0$, $y_K'=1 + 4=5$, so $K'(0,5)$
Assume $H( - 1,-1)$
$x_H'=-1+( - 3)=-4$, $y_H'=-1 + 4=3$, so $H'(-4,3)$
For $T_{(-5,1)}$, assume $U(4,2)$
$x_U'=4+( - 5)=-1$, $y_U'=2 + 1=3$, so $U'(-1,3)$
Assume $P(6,0)$
$x_P'=6+( - 5)=1$, $y_P'=0 + 1=1$, so $P'(1,1)$
For $T_{(-10,-3)}$, assume $B(5, - 2)$ again
$x_B'=5+( - 10)=-5$, $y_B'=-2+( - 3)=-5$, so $B'(-5,-5)$
Assume $X(1,1)$
$x_X'=1+( - 10)=-9$, $y_X'=1+( - 3)=-2$, so $X'(-9,-2)$
For $T_{(-3,3)}$, assume $K(3,1)$
$x_K'=3+( - 3)=0$, $y_K'=1 + 3=4$, so $K'(0,4)$
Assume $P(6,0)$
$x_P'=6+( - 3)=3$, $y_P'=0 + 3=3$, so $P'(3,3)$

Answer:

1. $E(2,3)\to E'(1,4)$, $B(5, - 2)\to B'(4,-1)$
2. $X(1,1)\to X'(4,3)$, $Y(0,0)\to Y'(3,2)$
3. $K(3,1)\to K'(0,5)$, $H( - 1,-1)\to H'(-4,3)$
4. $U(4,2)\to U'(-1,3)$, $P(6,0)\to P'(1,1)$
5. $B(5, - 2)\to B'(-5,-5)$, $X(1,1)\to X'(-9,-2)$
6. $K(3,1)\to K'(0,4)$, $P(6,0)\to P'(3,3)$

(Note: The original coordinates of the points are assumed based on a general - grid understanding. If the actual coordinates from the graph are different, the results will change accordingly.)