Question

(a) the arrows below show that the coordinates on the left are mapped to the coordinates on the right. fill in the blanks to give the coordinates after the translation. original coordinates → final coordinates ( d(-3,2) \to d(5,-2) ) ( e(-8,1) \to e(0,-3) ) ( f(-7,4) \to f(1,0) ) (b) choose the general rule below that describes the translation mapping ( \triangle def ) to ( \triangle def ). ( (x,y) \to (x - 4,y + 8) ) ( (x,y) \to (4x,-8y) ) ( (x,y) \to (8x,-4y) ) ( (x,y) \to (-4x,8y) ) ( (x,y) \to (-8x,4y) ) ( (x,y) \to (x + 4,y - 8) ) ( (x,y) \to (x + 8,y - 4) ) ( (x,y) \to (x - 8,y + 4) )

Explanation:

Step1: Find the change in x - coordinate

For point \(D\): original \(x=-3\), final \(x = 5\). The change in \(x\) is \(5-(-3)=8\).
For point \(E\): original \(x=-8\), final \(x = 0\). The change in \(x\) is \(0 - (-8)=8\).
For point \(F\): original \(x=-7\), final \(x = 1\). The change in \(x\) is \(1-(-7)=8\).

Step2: Find the change in y - coordinate

For point \(D\): original \(y = 2\), final \(y=-2\). The change in \(y\) is \(-2 - 2=-4\).
For point \(E\): original \(y = 1\), final \(y=-3\). The change in \(y\) is \(-3 - 1=-4\).
For point \(F\): original \(y = 4\), final \(y = 0\). The change in \(y\) is \(0 - 4=-4\).

Step3: Determine the translation rule

The translation rule for a point \((x,y)\) is \((x,y)\to(x + 8,y-4)\)

Answer:

The general rule that describes the translation mapping \(\triangle DEF\) to \(\triangle D'E'F'\) is \((x,y)\to(x + 8,y-4)\)