Question

example 4
triangle jkl has coordinates j(-1, 5), k(1, 2), and l(-3, -1). determine the coordinates of the vertices of the image after each transformation.

1. reflection in x - axis
2. reflection in y - axis
3. translation along the vector <5, -4>

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 $J(-1,5)$:
$J'=(-1,-5)$
For point $K(1,2)$:
$K'=(1,-2)$
For point $L(-3,-1)$:
$L'=(-3,1)$

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 $J(-1,5)$:
$J''=(1,5)$
For point $K(1,2)$:
$K''=(-1,2)$
For point $L(-3,-1)$:
$L''=(3,-1)$

Step3: Recall translation rule

When translating a point $(x,y)$ along the vector $\langle a,b
angle$, the transformation rule is $(x,y)\to(x + a,y + b)$. Here $a = 5$ and $b=-4$.
For point $J(-1,5)$:
$J'''=(-1 + 5,5-4)=(4,1)$
For point $K(1,2)$:
$K'''=(1 + 5,2-4)=(6,-2)$
For point $L(-3,-1)$:
$L'''=(-3 + 5,-1-4)=(2,-5)$

Answer:

1. $J'(-1,-5),K'(1,-2),L'(-3,1)$
2. $J''(1,5),K''(-1,2),L''(3,-1)$
3. $J'''(4,1),K'''(6,-2),L'''(2,-5)$