Question

y=-x
b(7,1) → b(-1,-7)
c(6,-6) → c(6,-6)
d(2,-5) → d(5,-2)
multiple-choice question
if the pre image is below the line of symmetry, then its image after the reflection over y=-x
is above y=-x.
stays below y=-x.
rewatch

Explanation:

Reflection over the line \( y = -x \) swaps and negates the coordinates \((x,y)\) to \((-y,-x)\). A pre - image below the line \( y=-x \) (meaning \( y < -x \) for its points) will have an image such that the relationship is reversed. Geometrically, reflection over a line is a symmetric transformation across that line. So a point below the line of symmetry will be above the line after reflection. For example, take a point like \( D(2,-5) \), its image is \( D'(5,-2) \). Checking the position relative to \( y=-x \): for \( D \), \( -5 < - 2 \) (so below \( y=-x \) as \( y=-5,x = 2\), \( -x=-2 \) and \( -5 < - 2\)); for \( D' \), \( -2>-5 \) (so above \( y=-x \) as \( y = - 2,x = 5\), \( -x=-5 \) and \( -2>-5\)).

Answer:

A. is above \( y=-x \)