Question

given points ( j(4,4) ), ( a(6,6) ), and ( r(5,2) ), graph ( \triangle jar ) and its reflection image across the given line.
( x=-1 )
choose the correct graph below.

Explanation:

Step1: Find the reflection of point \(J(4,4)\)

The formula for reflecting a point \((x,y)\) across the line \(x = a\) is \((2a - x,y)\). Here \(a=-1\), so for \(J(4,4)\), the reflection \(J'\) has \(x\)-coordinate \(2\times(-1)-4=-2 - 4=-6\), \(y\)-coordinate remains \(4\). So \(J'(-6,4)\)

Step2: Find the reflection of point \(A(6,6)\)

Using the formula \((2a - x,y)\) with \(a = - 1\) and \((x,y)=(6,6)\). The \(x\)-coordinate of the reflection \(A'\) is \(2\times(-1)-6=-2-6=-8\), \(y\)-coordinate remains \(6\). So \(A'(-8,6)\)

Step3: Find the reflection of point \(R(5,2)\)

Using the formula \((2a - x,y)\) with \(a=-1\) and \((x,y)=(5,2)\). The \(x\)-coordinate of the reflection \(R'\) is \(2\times(-1)-5=-2 - 5=-7\), \(y\)-coordinate remains \(2\). So \(R'(-7,2)\)

Step4: Check the graphs

Look for the graph where the original triangle \(JAR\) (with points \(J(4,4)\), \(A(6,6)\), \(R(5,2)\)) and its reflection (with points \(J'(-6,4)\), \(A'(-8,6)\), \(R'(-7,2)\)) are plotted correctly.

Answer:

A.