Question

question 26 (mandatory) (1 point)
which point(s) remain unchanged under a reflection in the x - axis?
a) the y - intercept
b) the x - intercepts
c) the point(s) where y = x
d) both the x - and y - intercepts

Explanation:

When reflecting a point \((x,y)\) over the \(x -\)axis, the transformation rule is \((x,y)\to(x, - y)\).

• For a \(y -\)intercept, its coordinates are \((0,y)\). After reflection over the \(x -\)axis, it becomes \((0,-y)\) (changes unless \(y = 0\)).
• For an \(x -\)intercept, its coordinates are \((x,0)\). After reflection over the \(x -\)axis, using the rule \((x,y)\to(x, - y)\), we get \((x,-0)=(x,0)\) (remains the same).
• For a point on \(y = x\) (coordinates \((a,a)\)), after reflection over the \(x -\)axis, it becomes \((a,-a)\) (changes unless \(a = 0\)).

Answer:

B. the \(x -\)intercepts