Question

question 3 (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:

Step1: Recall reflection rule

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

Step2: Analyze \(x -\)intercept

For an \(x -\)intercept, \(y = 0\). Let the point be \((a,0)\). After reflection over the \(x -\)axis, using the rule \((x,y)\to(x,-y)\), we get \((a,0)\) (since \(- 0=0\)).

Step3: Analyze \(y -\)intercept

For a \(y -\)intercept, \(x = 0\). Let the point be \((0,b)\). After reflection over the \(x -\)axis, using the rule \((x,y)\to(x,-y)\), we get \((0,-b)
eq(0,b)\) (if \(b
eq0\)).

Step4: Analyze \(y = x\) points

Let a point on \(y = x\) be \((c,c)\). After reflection over the \(x -\)axis, using the rule \((x,y)\to(x,-y)\), we get \((c,-c)
eq(c,c)\) (if \(c
eq0\)).

Answer:

B. the \(x -\)intercepts