Question

rhombus klmn with vertices k(-3, 2), l(1, 4), m(-1, 0), and n(-5, -2): (x, y) → (x + 2, y - 5) k(__, ) l(, ) m(, ) n(, __) find the new vertices given the translation properties.

Explanation:

Step1: Find new x - coordinate of K'

Given $K(-3,2)$ and translation $(x,y)\to(x + 2,y - 5)$. For $x$ - coordinate of $K'$, substitute $x=-3$ into $x+2$. So, $-3 + 2=-1$.

Step2: Find new y - coordinate of K'

Substitute $y = 2$ into $y-5$. So, $2-5=-3$. Thus, $K'(-1,-3)$.

Step3: Find new x - coordinate of L'

Given $L(1,4)$, for $x$ - coordinate of $L'$, substitute $x = 1$ into $x+2$. So, $1+2=3$.

Step4: Find new y - coordinate of L'

Substitute $y = 4$ into $y - 5$. So, $4-5=-1$. Thus, $L'(3,-1)$.

Step5: Find new x - coordinate of M'

Given $M(-1,0)$, for $x$ - coordinate of $M'$, substitute $x=-1$ into $x + 2$. So, $-1+2=1$.

Step6: Find new y - coordinate of M'

Substitute $y = 0$ into $y-5$. So, $0-5=-5$. Thus, $M'(1,-5)$.

Step7: Find new x - coordinate of N'

Given $N(-5,-2)$, for $x$ - coordinate of $N'$, substitute $x=-5$ into $x+2$. So, $-5+2=-3$.

Step8: Find new y - coordinate of N'

Substitute $y=-2$ into $y-5$. So, $-2-5=-7$. Thus, $N'(-3,-7)$.

Answer:

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