How are the properties of reflection used to
transform a figure?

The properties of reflection are used when we want to reflect a figure across a specific line, it can be across y-axis, x-axis, y = x or y = -x.

In either case, the result is a reflection, that is, those lines will work as a mirror, having the same shape and size but reflected across the line.

It's important to say that a reflection is a rigid transformation, which means the shape or size of the figure won't chance.

If we want to reflect across the y-axis, the transformation is:

Across the x-axis:

Across the line y = x:

Across the line y = -x: .

5.0

Step-by-step explanation:

Using Pythagorean Theorem:

a² + b² = c²

where a =? b= 12 in and c = 13 in

a² + (12)² = (13)²

a² + 144 = 169

a² = 169 - 144

a² = 25

a = √25 = 5

∴ a = 5.0

Pythagoras Theorem is usually applied when finding one missing side of a right-angle triangle.