Question

write the coordinates of the vertices after a reflection over the line $x=-1$.

Explanation:

Step1: Find the distance of each point from the line \(x = - 1\)

For a point \((x,y)\), the distance from the line \(x=-1\) is \(d=x - (-1)=x + 1\).

• For point \(J(-1,-3)\): The distance \(d=-1-(-1) = 0\).
• For point \(K(8,-3)\): The distance \(d=8-(-1)=9\).
• For point \(L(4,4)\): The distance \(d=4-(-1)=5\).
• For point \(M(0,4)\): The distance \(d=0-(-1)=1\).

Step2: Reflect the points over the line \(x = - 1\)

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a=-1\), so the formula is \((-2 - x,y)\)

• For \(J(-1,-3)\): \(x'=-2-(-1)=-1\), \(y'=-3\), so \(J'(-1,-3)\)
• For \(K(8,-3)\): \(x'=-2 - 8=-10\), \(y'=-3\), so \(K'(-10,-3)\)
• For \(L(4,4)\): \(x'=-2 - 4=-6\), \(y'=4\), so \(L'(-6,4)\)
• For \(M(0,4)\): \(x'=-2-0=-2\), \(y'=4\), so \(M'(-2,4)\)

Answer:

\(J'(-1,-3)\), \(K'(-10,-3)\), \(L'(-6,4)\), \(M'(-2,4)\)