Question

the following point was reflected across the $x-$axis, what would be the coordinates of the reflected point? $(-6,4)$
a $(-4,-4)$
b $(6,-4)$
c $(-6,4)$
d $(-6,-4)$

Explanation:

Step1: Recall reflection rule over x - axis

When a point \((x,y)\) is reflected across the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. The formula for the reflection of a point \((x,y)\) across the \(x\) - axis is \((x,-y)\).

Step2: Apply the rule to the given point

Given the point \((-6,4)\), here \(x=-6\) and \(y = 4\). After reflecting across the \(x\) - axis, the \(x\) - coordinate is still \(-6\) and the \(y\) - coordinate becomes \(-4\). So the reflected point is \((-6,-4)\)? Wait, no, wait. Wait, let's check the options again. Wait, the formula is: reflection over \(x\) - axis: \((x,y)\to(x, - y)\). So for \((-6,4)\), \(x=-6\), \(y = 4\), so the reflected point is \((-6,-4)\)? But wait, the options: option d is \((-6,-4)\). Wait, maybe I made a mistake earlier. Wait, let's re - check the options. The options are:
a. \((-4,-4)\)
b. \((6,-4)\)
c. \((-6,4)\)
d. \((-6,-4)\)

Wait, the original point is \((-6,4)\). When reflecting over the \(x\) - axis, the \(x\) - coordinate stays the same, the \(y\) - coordinate is negated. So \(x=-6\), \(y\) becomes \(-4\). So the reflected point is \((-6,-4)\), which is option d. Wait, but in the initial problem, the user's image shows option b as \((6,-4)\) (maybe a typo in my first analysis). Wait, no, let's re - derive. The rule for reflection over \(x\) - axis: for a point \((x,y)\), the reflection is \((x,-y)\). So for \((-6,4)\), \(x=-6\), \(y = 4\), so the reflection is \((-6,-4)\), which is option d. But let's check the options again. The options are:

a. \((-4,-4)\)

b. \((6,-4)\)

c. \((-6,4)\)

d. \((-6,-4)\)

So according to the reflection rule, the correct answer should be d. \((-6,-4)\). Wait, maybe I misread the options earlier. Let's confirm the rule: Reflection over \(x\) - axis: \((x,y)\to(x,-y)\). So \((-6,4)\) becomes \((-6,-4)\). So the correct option is d. \((-6,-4)\).

Answer:

d. \((-6,-4)\)