Question

find the new points for the translation of rectangle defg with vertices d(6, 1), e(8, 0), f(5, -6), and g(3, -5); (x, y) → (x - 11, y + 4)

Explanation:

Step1: Translate point D(6,1)

To translate a point \((x, y)\) using the rule \((x - 11, y + 4)\), we substitute \(x = 6\) and \(y = 1\) into the rule.
For the x - coordinate: \(6-11=-5\)
For the y - coordinate: \(1 + 4=5\)
So the new point \(D'\) is \((-5,5)\)

Step2: Translate point E(8,0)

Substitute \(x = 8\) and \(y = 0\) into the translation rule \((x - 11,y + 4)\)
For the x - coordinate: \(8-11=-3\)
For the y - coordinate: \(0 + 4 = 4\)
So the new point \(E'\) is \((-3,4)\)

Step3: Translate point F(5,-6)

Substitute \(x = 5\) and \(y=-6\) into the translation rule \((x - 11,y + 4)\)
For the x - coordinate: \(5-11=-6\)
For the y - coordinate: \(-6 + 4=-2\)
So the new point \(F'\) is \((-6,-2)\)

Step4: Translate point G(3,-5)

Substitute \(x = 3\) and \(y = - 5\) into the translation rule \((x - 11,y + 4)\)
For the x - coordinate: \(3-11=-8\)
For the y - coordinate: \(-5 + 4=-1\)
So the new point \(G'\) is \((-8,-1)\)

Answer:

The new points are \(D'(-5,5)\), \(E'(-3,4)\), \(F'(-6,-2)\), \(G'(-8,-1)\)