Question

1. rhombus klmn with vertices k(-3, 2), l(1, 4), m(-1, 0), and n(-5, -2): (x, y) → (x, y - 5)

Explanation:

Step1: Apply transformation to point K

Given $K(-3,2)$ and transformation $(x,y)\to(x,y - 5)$. Substitute $x=-3,y = 2$ into the transformation. So $y-5=2 - 5=-3$, and $x=-3$. Thus $K'(-3,-3)$.

Step2: Apply transformation to point L

Given $L(1,4)$ and transformation $(x,y)\to(x,y - 5)$. Substitute $x = 1,y=4$ into the transformation. So $y-5=4 - 5=-1$, and $x = 1$. Thus $L'(1,-1)$.

Step3: Apply transformation to point M

Given $M(-1,0)$ and transformation $(x,y)\to(x,y - 5)$. Substitute $x=-1,y = 0$ into the transformation. So $y-5=0 - 5=-5$, and $x=-1$. Thus $M'(-1,-5)$.

Step4: Apply transformation to point N

Given $N(-5,-2)$ and transformation $(x,y)\to(x,y - 5)$. Substitute $x=-5,y=-2$ into the transformation. So $y-5=-2 - 5=-7$, and $x=-5$. Thus $N'(-5,-7)$.

Answer:

$K'(-3,-3),L'(1,-1),M'(-1,-5),N'(-5,-7)$