Question

△abc is shown in the coordinate plane. it will be reflected across the x - axis to form △abc.
complete the table to show the coordinates of △abc and its image.
△abc △abc
a(-4,3) ?
b(-2,1)
c(-4,1)
a(-4,-3)
a(4,3)
a(-3,-4)
a(3,4)

Explanation:

Step1: Recall the reflection rule

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

Step2: Apply the rule to point \(A(-4,3)\)

For point \(A(-4,3)\), using the rule \((x,y)\to(x, - y)\), we substitute \(x=-4\) and \(y = 3\). Then the \(y -\)coordinate becomes \(-y=-3\). So the image of \(A(-4,3)\) is \(A'(-4,-3)\).

Step3: Apply the rule to point \(B(-2,1)\)

For point \(B(-2,1)\), substitute \(x =-2\) and \(y = 1\) into the rule \((x,y)\to(x, - y)\). The \(y -\)coordinate becomes \(-y=-1\). So the image of \(B(-2,1)\) is \(B'(-2,-1)\).

Step4: Apply the rule to point \(C(-4,1)\)

For point \(C(-4,1)\), substitute \(x=-4\) and \(y = 1\) into the rule \((x,y)\to(x, - y)\). The \(y -\)coordinate becomes \(-y=-1\). So the image of \(C(-4,1)\) is \(C'(-4,-1)\).

Answer:

\(\triangle ABC\)	\(\triangle A'B'C'\)
\(B(-2,1)\)	\(B'(-2,-1)\)
\(C(-4,1)\)	\(C'(-4,-1)\)