Question

write the coordinates for the transformation. examples and rules can be found on the canvas page under topic 3.

translations

1. t_(5, - 1) △abc, where a(0,3), b(2,5), and c(7,6)
2. t_(5,3) △abc, where a(0,3), b(2,5), and c(7,6)
3. t_(-5,8) △abc, where a(0,3), b(2,5), and c(7,6)
4. t_(-4,0) △abc, where a(0,3), b(2,5), and c(7,6)

reflections

1. r_m△abc, where a(3,0), b(5,3), and c(7,6) and line m is y = x.
2. r_m△abc, where a(3,0), b(5,3), and c(7,6) and line m is y = 0.
3. r_m△abc, where a(3,0), b(5,3), and c(7,6) and line m is x = 0.

Explanation:

Step1: Recall translation rule

For a translation $T_{(a,b)}(x,y)=(x + a,y + b)$.

Step2: Solve for 1. $T_{(5,1)}\triangle ABC$

For point $A(0,3)$: $A'=(0 + 5,3+1)=(5,4)$
For point $B(2,5)$: $B'=(2 + 5,5 + 1)=(7,6)$
For point $C(7,6)$: $C'=(7+5,6 + 1)=(12,7)$

Step3: Solve for 2. $T_{(5,3)}\triangle ABC$

For point $A(0,3)$: $A'=(0 + 5,3+3)=(5,6)$
For point $B(2,5)$: $B'=(2 + 5,5 + 3)=(7,8)$
For point $C(7,6)$: $C'=(7+5,6 + 3)=(12,9)$

Step4: Solve for 3. $T_{(- 5,8)}\triangle ABC$

For point $A(0,3)$: $A'=(0-5,3 + 8)=(-5,11)$
For point $B(2,5)$: $B'=(2-5,5 + 8)=(-3,13)$
For point $C(7,6)$: $C'=(7-5,6 + 8)=(2,14)$

Step5: Solve for 4. $T_{(-4,0)}\triangle ABC$

For point $A(0,3)$: $A'=(0-4,3+0)=(-4,3)$
For point $B(2,5)$: $B'=(2-4,5 + 0)=(-2,5)$
For point $C(7,6)$: $C'=(7-4,6 + 0)=(3,6)$

Step6: Recall reflection rule for $y = x$

$R_{y = x}(x,y)=(y,x)$
For 5. $R_{m}\triangle ABC$ where $m:y = x$ and $A(3,0),B(5,3),C(7,6)$
$A'=(0,3)$
$B'=(3,5)$
$C'=(6,7)$

Step7: Recall reflection rule for $y = 0$

$R_{y = 0}(x,y)=(x,-y)$
For 6. $R_{m}\triangle ABC$ where $m:y = 0$ and $A(3,0),B(5,3),C(7,6)$
$A'=(3,0)$
$B'=(5,-3)$
$C'=(7,-6)$

Step8: Recall reflection rule for $x = 0$

$R_{x = 0}(x,y)=(-x,y)$
For 7. $R_{m}\triangle ABC$ where $m:x = 0$ and $A(3,0),B(5,3),C(7,6)$
$A'=(-3,0)$
$B'=(-5,3)$
$C'=(-7,6)$

Answer:

1. $A'(5,4),B'(7,6),C'(12,7)$
2. $A'(5,6),B'(7,8),C'(12,9)$
3. $A'(-5,11),B'(-3,13),C'(2,14)$
4. $A'(-4,3),B'(-2,5),C'(3,6)$
5. $A'(0,3),B'(3,5),C'(6,7)$
6. $A'(3,0),B'(5,-3),C'(7,-6)$
7. $A'(-3,0),B'(-5,3),C'(-7,6)$