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 ) \\)
10

Explanation:

Step1: Find the distance from each point to the line \(x = 2\)

For point \(J(1,-1)\), the distance is \(|2 - 1|=1\).
For point \(K(3,0)\), the distance is \(|3 - 2| = 1\).
For point \(L(0,-4)\), the distance is \(|2-0|=2\).

Step2: Calculate the coordinates of the reflected points

For a reflection over the line \(x = 2\), the formula for the \(x\)-coordinate of a point \((x,y)\) is \(x'=2+(2 - x)\), and the \(y\)-coordinate remains the same \(y'=y\).

• For \(J(1,-1)\): \(x'=2+(2 - 1)=3\), \(y'=-1\), so \(J'(3,-1)\).
• For \(K(3,0)\): \(x'=2+(2 - 3)=1\), \(y' = 0\), so \(K'(1,0)\).
• For \(L(0,-4)\): \(x'=2+(2 - 0)=4\), \(y'=-4\), 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.