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: Reflection formula

For a reflection in the line \(x = a\), the formula is \((x,y)\to(2a - x,y)\). Here \(a = 5\).

Step2: Apply formula to point \(L(6,6)\)

Substitute \(x = 6\) and \(y = 6\) into \((2a - x,y)\).
\(2\times5-6=4\), so \(L'\) is \((4,6)\).

Step3: Apply formula to point \(M(8,8)\)

Substitute \(x = 8\) and \(y = 8\) into \((2a - x,y)\).
\(2\times5 - 8=2\), so \(M'\) is \((2,8)\).

Step4: Apply formula to point \(N(8,3)\)

Substitute \(x = 8\) and \(y = 3\) into \((2a - x,y)\).
\(2\times5 - 8 = 2\), so \(N'\) is \((2,3)\).

Answer:

\(L'(4,6)\), \(M'(2,8)\), \(N'(2,3)\)