Question

find measures using rigid transformations
triangle ( \triangle abc ) is rotated ( 135^{circ} ) about point ( s ) to create ( \triangle abc ).
what is the perimeter of ( \triangle abc )?
units

Explanation:

Step1: Recall the property of rigid transformation

Rigid transformations (such as rotation) preserve the shape and size of the figure. So, \(\triangle ABC\cong\triangle A'B'C'\).

Step2: Find the side - lengths of \(\triangle ABC\)

Since \(\triangle ABC\cong\triangle A'B'C'\), the side - lengths of \(\triangle ABC\) are \(AB = 6.1\), \(BC=2\), and \(AC = 6.8\).

Step3: Calculate the perimeter of \(\triangle ABC\)

The perimeter \(P\) of a triangle is \(P=a + b + c\) (where \(a\), \(b\), and \(c\) are the side - lengths of the triangle).
\(P=6.1 + 2+6.8\)
\(P=(6.1 + 6.8)+2\)
\(P = 12.9+2\)

Answer:

\(14.9\)