Question

graph \\( \triangle j k l \\) and its image after a reflection in the line \\( x = 2 \\)
\\( j ( 1, - 1 ), k ( 3, 0 ), l ( 0, - 4 ) \\)

Explanation:

Step1: Find the reflection formula

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a = 2\), so the formula is \((4 - x,y)\).

Step2: Reflect point \(J(1,-1)\)

Substitute \(x = 1,y=-1\) into \((4 - x,y)\).
\(4-1=3\), so \(J'(3,-1)\)

Step3: Reflect point \(K(3,0)\)

Substitute \(x = 3,y = 0\) into \((4 - x,y)\).
\(4 - 3=1\), so \(K'(1,0)\)

Step4: Reflect point \(L(0,-4)\)

Substitute \(x = 0,y=-4\) into \((4 - x,y)\).
\(4-0 = 4\), so \(L'(4,-4)\)

Answer:

Plot \(\triangle JKL\) with \(J(1,-1)\), \(K(3,0)\), \(L(0,-4)\) and \(\triangle J'K'L'\) with \(J'(3,-1)\), \(K'(1,0)\), \(L'(4,-4)\) on the coordinate - plane.