Question

algebra 2 cp
translations of shapes
graph the image of the figure using the transformation given.

1. translation: 1 unit left
2. translation: 1 unit right and 2 units down
3. translation: 3 units right
4. translation: 1 unit right and 2 units down
5. translation: 5 units up

u(-3, -4), m(-1, -1), l(-2, -5)

1. translation: 3 units up

r(-4, -3), d(-4, 0), l(0, 0), f(0, -3)

Explanation:

Step1: Identify original coordinates (1)

Original shape vertices: $V(2,0), Q(4,0), D(3,-3), U(2,-1)$

Step2: Apply translation (1, left 1)

New coordinates: $(x-1,y)$
$V'(2-1,0)=(1,0)$, $Q'(4-1,0)=(3,0)$, $D'(3-1,-3)=(2,-3)$, $U'(2-1,-1)=(1,-1)$

Step3: Identify original coordinates (2)

Original shape vertices: $T(-4,1), R(-1,1), I(-4,-1)$

Step4: Apply translation (2, right1 down2)

New coordinates: $(x+1,y-2)$
$T'(-4+1,1-2)=(-3,-1)$, $R'(-1+1,1-2)=(0,-1)$, $I'(-4+1,-1-2)=(-3,-3)$

Step5: Identify original coordinates (3)

Original shape vertices: $N(-3,2), M(-4,1), Q(-2,0), Z(0,0)$

Step6: Apply translation (3, right3)

New coordinates: $(x+3,y)$
$N'(-3+3,2)=(0,2)$, $M'(-4+3,1)=(-1,1)$, $Q'(-2+3,0)=(1,0)$, $Z'(0+3,0)=(3,0)$

Step7: Identify original coordinates (4)

Original shape vertices: $W(-2,1), E(0,2), G(-2,0)$

Step8: Apply translation (4, right1 down2)

New coordinates: $(x+1,y-2)$
$W'(-2+1,1-2)=(-1,-1)$, $E'(0+1,2-2)=(1,0)$, $G'(-2+1,0-2)=(-1,-2)$

Step9: Apply translation (5, up5)

New coordinates: $(x,y+5)$
$U(-3,-4)\to U'(-3,-4+5)=(-3,1)$, $M(-1,-1)\to M'(-1,-1+5)=(-1,4)$, $L(-2,-5)\to L'(-2,-5+5)=(-2,0)$

Step10: Apply translation (6, up3)

New coordinates: $(x,y+3)$
$R(-4,-3)\to R'(-4,-3+3)=(-4,0)$, $D(-4,0)\to D'(-4,0+3)=(-4,3)$, $L(0,0)\to L'(0,0+3)=(0,3)$, $F(0,-3)\to F'(0,-3+3)=(0,0)$

Answer:

1. Translated vertices: $V'(1,0)$, $Q'(3,0)$, $D'(2,-3)$, $U'(1,-1)$ (plot and connect these points)
2. Translated vertices: $T'(-3,-1)$, $R'(0,-1)$, $I'(-3,-3)$ (plot and connect these points)
3. Translated vertices: $N'(0,2)$, $M'(-1,1)$, $Q'(1,0)$, $Z'(3,0)$ (plot and connect these points)
4. Translated vertices: $W'(-1,-1)$, $E'(1,0)$, $G'(-1,-2)$ (plot and connect these points)
5. Translated vertices: $U'(-3,1)$, $M'(-1,4)$, $L'(-2,0)$ (plot and connect these points)
6. Translated vertices: $R'(-4,0)$, $D'(-4,3)$, $L'(0,3)$, $F'(0,0)$ (plot and connect these points)