Question

1. triangle lmn with vertices l(6, 6), m(8, 8), and n(8, 3): a) reflection in the line x = 5 b) 270° counterclockwise rotation about the origin l(_, _) m(_, _) n(_, _)

Explanation:

Step1: Find reflection in line x = 5

The formula for reflecting a point $(x,y)$ in the line $x = a$ is $(2a - x,y)$.
For point $L(6,6)$:
$x = 6$, $a = 5$, then $2a - x=2\times5 - 6 = 4$, so $L'=(4,6)$.
For point $M(8,8)$:
$x = 8$, $a = 5$, then $2a - x=2\times5 - 8 = 2$, so $M'=(2,8)$.
For point $N(8,3)$:
$x = 8$, $a = 5$, then $2a - x=2\times5 - 8 = 2$, so $N'=(2,3)$.

Step2: Find 270 - degree counter - clockwise rotation about origin

The rule for a 270 - degree counter - clockwise rotation about the origin $(x,y)\to(y,-x)$.
For $L'(4,6)$:
After rotation, $L''=(6,-4)$.
For $M'(2,8)$:
After rotation, $M''=(8,-2)$.
For $N'(2,3)$:
After rotation, $N''=(3,-2)$.

Answer:

$L'(4,6)$
$M'(2,8)$
$N'(2,3)$
(For the second - part rotation results: $L''=(6,-4)$, $M''=(8,-2)$, $N''=(3,-2)$)