Question

question 1 (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

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

Step2: Analyze each option

• Option a: The \(y\) - intercept is a point of the form \((0,y)\). After reflection over the \(x\) - axis, it becomes \((0,-y)

eq(0,y)\) (unless \(y = 0\)).

• Option b: The \(x\) - intercept is a point of the form \((x,0)\). After reflection over the \(x\) - axis, using the rule \((x,y)\to(x, - y)\), we get \((x,0)\to(x,0)\) (since \(-0 = 0\)).
• Option c: Points where \(y=x\) are of the form \((a,a)\). After reflection over the \(x\) - axis, they become \((a,-a)

eq(a,a)\) (unless \(a = 0\)).

• Option d: As shown in option a, \(y\) - intercepts (except when \(y = 0\)) change.

Answer:

B. the \(x\) - intercepts