Question

△rst is shown in the coordinate plane. it will be reflected across the y-axis to form △rst. complete the table to show the coordinates of △rst and its image. △rst: r(1, -4), s(3, -4), t(4, -2); △rst:? (for each vertex)

Explanation:

Step1: Recall reflection over y - axis rule

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

Step2: Find \(R'\)

For point \(R(1, - 4)\), using the reflection rule, \(x = 1\), so the new \(x\) - coordinate is \(-1\) and the \(y\) - coordinate remains \(-4\). So \(R'(-1,-4)\).

Step3: Find \(S'\)

For point \(S(3,-4)\), using the reflection rule, \(x = 3\), so the new \(x\) - coordinate is \(-3\) and the \(y\) - coordinate remains \(-4\). So \(S'(-3,-4)\).

Step4: Find \(T'\)

For point \(T(4,-2)\), using the reflection rule, \(x = 4\), so the new \(x\) - coordinate is \(-4\) and the \(y\) - coordinate remains \(-2\). So \(T'(-4,-2)\).

Answer:

For \(R(1,-4)\), \(R'(-1,-4)\); for \(S(3,-4)\), \(S'(-3,-4)\); for \(T(4,-2)\), \(T'(-4,-2)\)

So the completed table is:

\(\triangle RST\)	\(\triangle R'S'T'\)
\(S(3,-4)\)	\(S'(-3,-4)\)
\(T(4,-2)\)	\(T'(-4,-2)\)