Question

21 reflect over the x - axis. click to select polygon abc

Explanation:

Step1: Recall the reflection rule

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

Step2: Find the coordinates of points \(A\), \(B\), and \(C\)

From the graph, assume \(A=(1,3)\), \(B=(2,2)\), \(C=(5,2)\).

Step3: Apply the reflection rule

For point \(A\):
Using the rule \((x,y)\to(x, - y)\), when \(x = 1\) and \(y=3\), \(A'=(1,- 3)\).
For point \(B\):
When \(x = 2\) and \(y = 2\), \(B'=(2,-2)\).
For point \(C\):
When \(x = 5\) and \(y = 2\), \(C'=(5,-2)\).

Step4: Plot the new polygon \(A'B'C'\)

Plot the points \(A'(1,-3)\), \(B'(2,-2)\) and \(C'(5,-2)\) and connect them to form the reflected polygon.

Answer:

Plot the points \(A'(1,-3)\), \(B'(2,-2)\) and \(C'(5,-2)\) and connect them to get the polygon \(A'B'C'\) which is the reflection of polygon \(ABC\) over the \(x -\)axis.