Question

Triangle HAM is reflected over the y-axis using the rule (x, y) → (−x, y) to create triangle H′A′M′. If a line segment is drawn from point A to point A′, which statement would best describe the line segment drawn in relation to the y-axis?

a
They create concentric circles.

b
They are parallel to each other.

c
The y-axis is a bisector of the segment drawn.

d
The segment drawn and the y-axis are congruent to each other.

Answer 1

Answer:
The line segment which is drawn from point A to point A′ is perpendicular to the y-axis
Explanation:
* Lets explain the meaning of reflection in mathematics
- Reflection is a transformation where each point in a shape appears at
an equal distance on the opposite side of a the line of reflection
- That line is called the axis of reflection
- When a figure is reflected, the line of reflection is the perpendicular
bisector of all segments that connect the image points to their
corresponding image points
- If point (x , y) reflected across the x-axis
∴ Its image is (x , -y)
- If point (x , y) reflected across the y-axis
∴ Its image is (-x , y)
- If point (x , y) reflected across the line y = x
∴ Its image is (y , x)
- If point (x , y) reflected across the line y = -x
∴ Its image is (-y , -x)
- If point (x , y) reflected across the origin (0 , 0)
∴ Its image is (-x , -y)
* Lets solve the problem
∵ Triangle HAM is reflected over the y-axis using the rule
(x , y) → (-x , y) to create triangle H′A′M′
∴ The line of the reflection is the y-axis
∵ The line of reflection is the perpendicular bisector of all segments
that connect the image points to their corresponding image points
∴ The y-axis is perpendicular bisector to the line AA'
∴ AA' ⊥ y-axis
∴ The line segment which is drawn from point A to point A′ is
perpendicular to the y-axis