Question

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

name each vector, then write the vector in component

Explanation:

Step1: Apply transformation to point K

Given point $K(-3,2)$ and transformation $(x,y)\to(x,y - 5)$. For $x=-3$ and $y = 2$, we calculate $y-5=2 - 5=-3$. So $K'$ is $(-3,-3)$.

Step2: Apply transformation to point L

Given point $L(1,4)$. Using the transformation $(x,y)\to(x,y - 5)$, for $x = 1$ and $y=4$, we have $y-5=4 - 5=-1$. So $L'$ is $(1,-1)$.

Step3: Apply transformation to point M

Given point $M(-1,0)$. With the transformation $(x,y)\to(x,y - 5)$, for $x=-1$ and $y = 0$, we get $y-5=0 - 5=-5$. So $M'$ is $(-1,-5)$.

Step4: Apply transformation to point N

Given point $N(-5,-2)$. Using the transformation $(x,y)\to(x,y - 5)$, for $x=-5$ and $y=-2$, we calculate $y-5=-2-5=-7$. So $N'$ is $(-5,-7)$.

Answer:

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