Question

1. quadrilateral stuv with vertices s(-3, -3), t(3, -5), u(6, -7), and v(-2, -7): y = -4

Explanation:

Step1: Find the reflection formula

When reflecting a point \((x,y)\) over the line \(y = k\), the formula is \((x,2k - y)\). Here \(k=-4\), so the formula is \((x,2\times(-4)-y)=(x,-8 - y)\)

Step2: Calculate \(S'\)

For \(S(-3,-3)\), \(x=-3,y = - 3\). Using the formula \((x,-8 - y)\), we get \(S'(-3,-8-(-3))=(-3,-5)\)

Step3: Calculate \(T'\)

For \(T(3,-5)\), \(x = 3,y=-5\). Using the formula \((x,-8 - y)\), we get \(T'(3,-8-(-5))=(3,-3)\)

Step4: Calculate \(U'\)

For \(U(6,-7)\), \(x = 6,y=-7\). Using the formula \((x,-8 - y)\), we get \(U'(6,-8-(-7))=(6,-1)\)

Step5: Calculate \(V'\)

For \(V(-2,-7)\), \(x=-2,y = - 7\). Using the formula \((x,-8 - y)\), we get \(V'(-2,-8-(-7))=(-2,-1)\)

Answer:

\(S'(-3,-5)\)
\(T'(3,-3)\)
\(U'(6,-1)\)
\(V'(-2,-1)\)