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: a(-4,3), b(-2,1), c(-4,1); △abc:? for each vertex.

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) across the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So, the image of the point \((x,y)\) after reflection over the \(x\) - axis is \((x, - y)\).

Step2: Find the image of point A

For point \(A(-4,3)\), using the reflection rule over the \(x\) - axis (\(x\) remains, \(y\) changes sign), we substitute \(x=-4\) and \(y = 3\) into the rule. So the coordinates of \(A'\) are \((-4,-3)\).

Step3: Find the image of point B

For point \(B(-2,1)\), using the reflection rule over the \(x\) - axis, the \(x\) - coordinate \(x=-2\) remains the same and the \(y\) - coordinate \(y = 1\) changes its sign. So the coordinates of \(B'\) are \((-2,-1)\).

Step4: Find the image of point C

For point \(C(-4,1)\), using the reflection rule over the \(x\) - axis, the \(x\) - coordinate \(x = - 4\) remains the same and the \(y\) - coordinate \(y=1\) changes its sign. So the coordinates of \(C'\) are \((-4,-1)\).

Answer:

For \(A(-4,3)\), \(A'(-4,-3)\); for \(B(-2,1)\), \(B'(-2,-1)\); for \(C(-4,1)\), \(C'(-4,-1)\)

So the completed table is:

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