A double reflection of a pre-image across perpendicular lines produce the same result, as
1:scaled dilation
2:180 rotation
3:90-degree rotation
4:270-degree rotation
The correct answer is 2: 180 rotation.
A double reflection is equivalent to a 180 rotation because each reflection flips the pre-image across the line of reflection, resulting in a 180-degree change in orientation. This means that if a pre-image is reflected across two perpendicular lines, it will essentially be rotated 180 degrees.
The correct answer is 1: scaled dilation.
To understand why a double reflection of a pre-image across perpendicular lines produces the same result, it's important to understand the properties of reflection and the concept of perpendicularity.
Reflection is a transformation that flips a figure over a line, called the line of reflection. It creates a mirror image of the original figure. When a figure is reflected twice, it means it is flipped twice, resulting in a double reflection.
Perpendicular lines are lines that intersect at a right angle, forming a 90-degree angle. The property of perpendicularity means that the lines are at right angles to each other.
Now let's go through each option and analyze its effect on a figure:
1. Scaled dilation: This transformation involves resizing or scaling a figure while keeping its shape. A double reflection across perpendicular lines does not result in a scaled dilation because dilation changes the size of the figure.
2. 180-degree rotation: A 180-degree rotation means rotating a figure by half a circle. When a figure is reflected twice across perpendicular lines, it results in a 180-degree rotation. This is because the double reflection flips the figure twice, effectively rotating it by 180 degrees.
3. 90-degree rotation: A 90-degree rotation involves rotating the figure by a quarter turn. A double reflection across perpendicular lines does not result in a 90-degree rotation. Instead, it produces a 180-degree rotation, as mentioned earlier.
4. 270-degree rotation: A 270-degree rotation means rotating the figure by three-quarters of a turn. A double reflection across perpendicular lines does not result in a 270-degree rotation. Instead, it produces a 180-degree rotation.
In summary, a double reflection of a pre-image across perpendicular lines produces a 180-degree rotation, which is option 2.