Question

write the coordinates of the vertices after a reflection over the line x = 4.

Explanation:

1. First, assume the coordinates of the vertices of the square are:

• Let's assume the coordinates of the vertices of the square \(JKLM\) are \(J(6, - 9)\), \(K(8,-9)\), \(L(8, - 8)\), \(M(6,-8)\) (by observing the grid - points).
• The formula for reflecting a point \((x,y)\) over the vertical line \(x = a\) is \((2a - x,y)\). Here \(a = 4\).

1. For point \(J(6,-9)\):

• Calculate the new \(x\) - coordinate using the formula \(x'=2a - x\). Substitute \(a = 4\) and \(x = 6\) into the formula.
• \(x'=2\times4−6=8 - 6=2\), and the \(y\) - coordinate remains the same \(y'=-9\). So the new coordinates of \(J\) are \((2,-9)\).

1. For point \(K(8,-9)\):

• Substitute \(a = 4\) and \(x = 8\) into the formula \(x'=2a - x\).
• \(x'=2\times4−8=8 - 8 = 0\), and \(y'=-9\). So the new coordinates of \(K\) are \((0,-9)\).

1. For point \(L(8,-8)\):

• Substitute \(a = 4\) and \(x = 8\) into the formula \(x'=2a - x\).
• \(x'=2\times4−8=0\), and \(y'=-8\). So the new coordinates of \(L\) are \((0,-8)\).

1. For point \(M(6,-8)\):

• Substitute \(a = 4\) and \(x = 6\) into the formula \(x'=2a - x\).
• \(x'=2\times4−6=2\), and \(y'=-8\). So the new coordinates of \(M\) are \((2,-8)\).

Step1: Identify reflection formula

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

Step2: Reflect point \(J(6,-9)\)

Substitute \(x = 6\) into \(2a - x\) with \(a = 4\). \(2\times4−6 = 2\), \(y\) - coordinate stays \(-9\). New coordinates are \((2,-9)\).

Step3: Reflect point \(K(8,-9)\)

Substitute \(x = 8\) into \(2a - x\) with \(a = 4\). \(2\times4−8 = 0\), \(y\) - coordinate stays \(-9\). New coordinates are \((0,-9)\).

Step4: Reflect point \(L(8,-8)\)

Substitute \(x = 8\) into \(2a - x\) with \(a = 4\). \(2\times4−8 = 0\), \(y\) - coordinate stays \(-8\). New coordinates are \((0,-8)\).

Step5: Reflect point \(M(6,-8)\)

Substitute \(x = 6\) into \(2a - x\) with \(a = 4\). \(2\times4−6 = 2\), \(y\) - coordinate stays \(-8\). New coordinates are \((2,-8)\).

Answer:

The new coordinates of the vertices are \(J(2,-9)\), \(K(0,-9)\), \(L(0,-8)\), \(M(2,-8)\)