Question

select the correct answer from each drop - down menu.
quadrilateral uvwx is reflected over the x - axis to form quadrilateral uvwx.
if vertex u is located at (-4, 5) and vertex v is located at (-6, 2), then vertex u is located at
and vertex v is located at
(options for u: (-4, 5), (4, -5), (-4, -5), (4, 5))

Explanation:

Step1: Recall reflection over x - axis rule

The rule for reflecting a point \((x,y)\) over the \(x\) - axis is that the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. So, if we have a point \((x,y)\), after reflection over the \(x\) - axis, the new point \((x',y')\) is given by \(x'=x\) and \(y'=-y\).

Step2: Find the coordinates of \(U'\)

Given that the coordinates of vertex \(U\) are \((-4,5)\). Using the reflection rule over the \(x\) - axis (\(x' = x\), \(y'=-y\)), for \(x=-4\) and \(y = 5\), we get \(x'=-4\) and \(y'=-5\). So the coordinates of \(U'\) are \((-4,-5)\).

Step3: Find the coordinates of \(V'\)

Given that the coordinates of vertex \(V\) are \((-6,2)\). Using the reflection rule over the \(x\) - axis (\(x'=x\), \(y' = -y\)), for \(x=-6\) and \(y = 2\), we get \(x'=-6\) and \(y'=-2\). So the coordinates of \(V'\) are \((-6,-2)\).

Answer:

The coordinates of \(U'\) are \((-4,-5)\) and the coordinates of \(V'\) are \((-6,-2)\). For the first drop - down (for \(U'\)) the correct option is \((-4,-5)\). For the second drop - down (for \(V'\)) the correct option (assuming the options are similar in structure) would be \((-6,-2)\) (if we follow the same reflection rule).