Question

write the set of coordinates for a reflection over the x-axis of the figure with the following vertices. (2,1),(5,1),(2,4) a (-2,1),(-5,1),(-2,4) b (-2,-1),(-5,-1),(-2,-4) c (2,-1),(5,-1),(2,-4) d (1,2),(1,5),(4,2)

Explanation:

Step1: Recall reflection over x - axis rule

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

Step2: Apply the rule to each vertex

• For the point \((2,1)\): Using the rule \((x,y)\to(x, - y)\), we substitute \(x = 2\) and \(y = 1\). So the reflected point is \((2,-1)\).
• For the point \((5,1)\): Substituting \(x = 5\) and \(y = 1\) into the rule \((x,y)\to(x, - y)\), we get \((5,-1)\).
• For the point \((2,4)\): Substituting \(x = 2\) and \(y = 4\) into the rule \((x,y)\to(x, - y)\), we get \((2,-4)\).

Answer:

c. \((2, - 1),(5, - 1),(2, - 4)\)