Question

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

Explanation:

Step1: Recall reflection rule

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

Step2: Analyze \(x -\)intercept

For an \(x -\)intercept, \(y = 0\). If \(y = 0\), then after reflection over the \(x -\)axis \((x,0)\to(x,0)\) (since \(-0=0\)).

Step3: Analyze \(y -\)intercept

For a \(y -\)intercept, \(x = 0\). If \((0,y)\) is reflected over the \(x -\)axis, it becomes \((0,-y)
eq(0,y)\) (unless \(y = 0\)).

Step4: Analyze \(y=x\) points

Let a point on \(y = x\) be \((a,a)\). After reflection over the \(x -\)axis, it becomes \((a,-a)\). If \(a
eq0\), \((a,-a)
eq(a,a)\).

Answer:

B. the \(x -\)intercepts