Question

complete the table to show the coordinates of \\( \triangle r s t \\) and its image.
\\( \

$$\begin{array} { | c | c | } { \\hline \\text { (1) } \\triangle r s t } & { \\text { (1) } \\triangle r ^ { \\prime } s ^ { \\prime } t ^ { \\prime } } \\\\ \\hline r ( 1, - 4 ) & {? } \\\\ \\hline s ( 3, - 4 ) & {? } \\\\ \\hline t ( 4, - 2 ) & {? } \\\\ \\hline \\end{array}$$

\\)

Explanation:

Step1: Recall the rule for reflection over the y - axis

When a point \((x,y)\) is reflected over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).

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

For point \(R(1, - 4)\), using the reflection rule \(x = 1\) becomes \(-x=-1\) and \(y=-4\) remains the same. So \(R'\) has coordinates \((-1,-4)\).

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

For point \(S(3,-4)\), using the reflection rule \(x = 3\) becomes \(-x=-3\) and \(y = - 4\) remains the same. So \(S'\) has coordinates \((-3,-4)\).

Step4: Find the coordinates of \(T'\)

For point \(T(4,-2)\), using the reflection rule \(x = 4\) becomes \(-x=-4\) and \(y=-2\) remains the same. So \(T'\) has coordinates \((-4,-2)\).

Answer:

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