Question

write the set of coordinates for a reflection over the x-axis of the figure with the following vertices. (1,3),(2,5),(3,2) a (-1,-3),(-2,-5),(-3,-2) b (-1,3),(-2,5),(-3,2) c (3,1),(5,2),(2,3) d (1,-3),(2,-5),(3,-2)

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is \((x,-y)\). That is, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign.

Step2: Apply the rule to each vertex

• For the point \((1,3)\): Using the rule \((x,-y)\), we substitute \(x = 1\) and \(y=3\). So the reflected point is \((1,- 3)\).
• For the point \((2,5)\): Using the rule \((x,-y)\), we substitute \(x = 2\) and \(y = 5\). So the reflected point is \((2,-5)\).
• For the point \((3,2)\): Using the rule \((x,-y)\), we substitute \(x=3\) and \(y = 2\). So the reflected point is \((3,-2)\).

Answer:

d. \((1, - 3),(2, - 5),(3, - 2)\)