Question

the vertices of triangle abc are (3, - 3), (1, 6), and (4, 3). identify the reflected coordinate points across the x-axis.\
\
\bigcirc a = (3, 3), b = (1, - 6), c = (4, - 3)\
\
\bigcirc a = (- 3, - 3), b = (- 1, 6), c = (- 4, 3)\
\
\bigcirc a = (- 3, 3), b = (1, 6), c = (4, 3)\
\
\bigcirc a = (- 3, 3), b = (- 1, - 6), c = (- 4, - 3)

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is \((x,y)\to(x, - y)\). This means that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign.

Step2: Reflect point \(A(3,-3)\)

For point \(A=(3,-3)\), applying the reflection rule over the \(x\) - axis: \(x = 3\) (remains the same), \(y=-3\) changes to \(-(-3)=3\). So \(A'=(3,3)\).

Step3: Reflect point \(B(1,6)\)

For point \(B=(1,6)\), applying the reflection rule: \(x = 1\) (remains the same), \(y = 6\) changes to \(-6\). So \(B'=(1,-6)\).

Step4: Reflect point \(C(4,3)\)

For point \(C=(4,3)\), applying the reflection rule: \(x = 4\) (remains the same), \(y = 3\) changes to \(-3\). So \(C'=(4,-3)\).

Answer:

A. \(A'=(3, 3), B'=(1, - 6), C'=(4, - 3)\)