Question

question 36 (mandatory) (1 point) retake question 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 reflecting a point \((x,y)\) over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).

Step2: Analyze intercepts

• For \(y\) - intercept: A \(y\) - intercept has coordinates \((0,y)\). After reflection over the \(x\) - axis, it becomes \((0,-y)\) (changes unless \(y = 0\)).
• For \(x\) - intercept: An \(x\) - intercept has coordinates \((x,0)\). After reflection over the \(x\) - axis, using the rule \((x,y)\to(x, - y)\), we get \((x,0)\) (since \(-0=0\)).

Answer:

B. the \(x\) - intercepts