Question

graph \\( \triangle a b c \\) with vertices \\( a ( - 5, - 6 ), b ( - 4, - 3 ) \\), and \\( c ( - 3, - 7 ) \\) and its image after a reflection in the line \\( x = - 3 \\).

Explanation:

Step1: Recall the reflection formula

When reflecting a point \((x,y)\) over the line \(x = a\), the formula is \((x',y')=(2a - x,y)\)

Step2: Find the image of point \(A(-5,-6)\)

Here \(a=-3\), \(x=-5\), \(y = - 6\)
Using the formula \(x'=2\times(-3)-(-5)=-6 + 5=-1\), \(y'=-6\)
So \(A'(-1,-6)\)

Step3: Find the image of point \(B(-4,-3)\)

Here \(a=-3\), \(x=-4\), \(y=-3\)
Using the formula \(x'=2\times(-3)-(-4)=-6 + 4=-2\), \(y'=-3\)
So \(B'(-2,-3)\)

Step4: Find the image of point \(C(-3,-7)\)

Here \(a=-3\), \(x=-3\), \(y=-7\)
Using the formula \(x'=2\times(-3)-(-3)=-6+3=-3\), \(y'=-7\)
So \(C'(-3,-7)\)

Answer:

The vertices of the image \(\triangle A'B'C'\) are \(A'(-1,-6)\), \(B'(-2,-3)\) and \(C'(-3,-7)\)