Question

directions: graph and label each figure and its image under the given translation. give the new coordinates.

1. trapezoid ( xyzw ) with vertices ( s(-3,6)), ( t(0,7)), ( u(1,4)), and ( v(5,2)); ((x,y)\to(x + 7,y - 9))
2. triangle ( abc ) with vertices ( a(0,7)), ( b(7,3)), and ( c(1,4)); ((x,y)\to(x - 3,y - 4))
3. rhombus ( klmn ) with vertices ( k(-3,2)), ( l(1,4)), ( m(-1,0)), and ( n(-5,-2)); ((x,y)\to(x + 2,y - 5))
4. rectangle ( defg ) with vertices ( d(-4,3)), ( e(0,2)), ( f(-2,-6)), and ( g(-6,-5)); ((x,y)\to(x + 4,y + 1))

directions: write a rule describing each translation below.
5.
6.

Explanation:

Step1: Apply translation rule for trapezoid

For trapezoid $STUV$ with translation $(x,y)\to(x + 7,y - 9)$:
For $S(3,6)$: $S'(3 + 7,6-9)=(10,-3)$
For $T(0,7)$: $T'(0 + 7,7-9)=(7,-2)$
For $U(1,4)$: $U'(1 + 7,4-9)=(8,-5)$
For $V(5,2)$: $V'(5 + 7,2-9)=(12,-7)$

Step2: Apply translation rule for triangle

For triangle $ABC$ with translation $(x,y)\to(x - 3,y - 4)$:
For $A(0,7)$: $A'(0-3,7 - 4)=(-3,3)$
For $B(7,3)$: $B'(7-3,3 - 4)=(4,-1)$
For $C(1,4)$: $C'(1-3,4 - 4)=(-2,0)$

Step3: Apply translation rule for rhombus

For rhombus $KLMN$ with translation $(x,y)\to(x + 2,y - 5)$:
For $K(-3,2)$: $K'(-3 + 2,2-5)=(-1,-3)$
For $L(1,4)$: $L'(1 + 2,4-5)=(3,-1)$
For $M(-1,0)$: $M'(-1 + 2,0-5)=(1,-5)$
For $N(-5,-2)$: $N'(-5 + 2,-2-5)=(-3,-7)$

Step4: Apply translation rule for rectangle

For rectangle $DEFG$ with translation $(x,y)\to(x + 4,y + 1)$:
For $D(-4,3)$: $D'(-4 + 4,3+1)=(0,4)$
For $E(0,2)$: $E'(0 + 4,2+1)=(4,3)$
For $F(-2,-6)$: $F'(-2 + 4,-6+1)=(2,-5)$
For $G(-6,-5)$: $G'(-6 + 4,-5+1)=(-2,-4)$

Step5: Determine translation rule for 5

Count the horizontal and vertical changes from pre - image to image. Let's assume two corresponding points. If we observe carefully, for a point in pre - image $(x,y)$ and its corresponding point in image, the horizontal change is $x'=x - 4$ and the vertical change is $y'=y-3$. So the rule is $(x,y)\to(x - 4,y - 3)$

Step6: Determine translation rule for 6

Count the horizontal and vertical changes from pre - image to image. For a point in pre - image $(x,y)$ and its corresponding point in image, the horizontal change is $x'=x+3$ and the vertical change is $y'=y - 2$. So the rule is $(x,y)\to(x + 3,y - 2)$

Answer:

1. $S'(10,-3)$, $T'(7,-2)$, $U'(8,-5)$, $V'(12,-7)$
2. $A'(-3,3)$, $B'(4,-1)$, $C'(-2,0)$
3. $K'(-1,-3)$, $L'(3,-1)$, $M'(1,-5)$, $N'(-3,-7)$
4. $D'(0,4)$, $E'(4,3)$, $F'(2,-5)$, $G'(-2,-4)$
5. $(x,y)\to(x - 4,y - 3)$
6. $(x,y)\to(x + 3,y - 2)$