Question

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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 (-4, -5) and vertex v is located at
options for v: (-6, -2), (6, 2), (6, -2), (-6, 2)
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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. Mathematically, if a point \(P=(x,y)\) is reflected over the \(x\) - axis, the image \(P'=(x, - y)\).

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

Given that vertex \(U\) is located at \((-4,5)\). Using the reflection rule over the \(x\) - axis (\(x\) - coordinate stays the same, \(y\) - coordinate is negated), for the point \(U(-4,5)\), the \(x\) - coordinate \(x=-4\) remains unchanged, and the \(y\) - coordinate \(y = 5\) becomes \(y=-5\). So, the coordinates of \(U'\) are \((-4,-5)\).

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

Given that vertex \(V\) is located at \((-6,2)\). Using the reflection rule over the \(x\) - axis, the \(x\) - coordinate \(x = - 6\) remains unchanged, and the \(y\) - coordinate \(y=2\) becomes \(y=-2\). So, the coordinates of \(V'\) are \((-6,-2)\).

Answer:

Vertex \(U'\) is located at \((-4, - 5)\) and vertex \(V'\) is located at \((-6, - 2)\)