Question

name
transformations in the plane - practice
examples 1 and 2

1. identify the type of transformation shown as a reflection, translation, or rotation.

2.
3.
4.
5.
6.
example 3
triangle abc has coordinates a(2, 0), b(-1, 5), and c(4, 3). determine the coordinates of vertices of the image after each transformation.

1. reflection in x - axis
2. reflection in y - axis
3. translation along the vector <1, 0>
4. translation along the vector <-3, 1>

Explanation:

Step1: Recall reflection rule for x - axis

When reflecting a point $(x,y)$ in the x - axis, the transformation rule is $(x,y)\to(x, - y)$.
For point $A(2,0)$:
$A'(2,0\times(- 1))=(2,0)$
For point $B(-1,5)$:
$B'(-1,5\times(-1))=(-1,-5)$
For point $C(4,3)$:
$C'(4,3\times(-1))=(4,-3)$

Step2: Recall reflection rule for y - axis

When reflecting a point $(x,y)$ in the y - axis, the transformation rule is $(x,y)\to(-x,y)$.
For point $A(2,0)$:
$A''(-2,0)$
For point $B(-1,5)$:
$B''(1,5)$
For point $C(4,3)$:
$C''(-4,3)$

Step3: Recall translation rule for vector $\langle1,0

angle$
When translating a point $(x,y)$ along the vector $\langle a,b
angle=(1,0)$ here, the rule is $(x,y)\to(x + a,y + b)$.
For point $A(2,0)$:
$A'''(2 + 1,0+0)=(3,0)$
For point $B(-1,5)$:
$B'''(-1 + 1,5+0)=(0,5)$
For point $C(4,3)$:
$C'''(4 + 1,3+0)=(5,3)$

Step4: Recall translation rule for vector $\langle-3,1

angle$
When translating a point $(x,y)$ along the vector $\langle a,b
angle=\langle-3,1
angle$, the rule is $(x,y)\to(x + a,y + b)$.
For point $A(2,0)$:
$A''''(2+( - 3),0 + 1)=(-1,1)$
For point $B(-1,5)$:
$B''''(-1+( - 3),5 + 1)=(-4,6)$
For point $C(4,3)$:
$C''''(4+( - 3),3 + 1)=(1,4)$

Answer:

1. $A'(2,0),B'(-1,-5),C'(4,-3)$
2. $A''(-2,0),B''(1,5),C''(-4,3)$
3. $A'''(3,0),B'''(0,5),C'''(5,3)$
4. $A''''(-1,1),B''''(-4,6),C''''(1,4)$