Question

question 33 (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 the rule for reflection over the x - axis

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

Step2: Analyze each option

• Option a: For a \(y\) - intercept, the point is of the form \((0,y)\). After reflection over the \(x\) - axis, it becomes \((0, - y)\). So it changes.
• Option b: For an \(x\) - intercept, the point is of the form \((x,0)\). After reflection over the \(x\) - axis, using the rule \((x,y)\to(x, - y)\), we get \((x,-0)=(x,0)\). So \(x\) - intercepts remain unchanged.
• Option c: Points where \(y = x\) are of the form \((a,a)\). After reflection over the \(x\) - axis, they become \((a,-a)\) (unless \(a = 0\)). So they change in general.
• Option d: Since \(y\) - intercepts change (as shown in option a), this option is incorrect.

Answer:

B. the \(x\) - intercepts