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(2,5) \to d(-4,-2) ) ( e(1,8) \to e(-5,1) ) ( f(5,4) \to f(-1,-3) ) (b) choose the general rule below that describes the translation mapping ( \triangle def ) to ( \triangle def ). ( (x,y) \to (-6x,-7y) ) ( (x,y) \to (-7x,-6y) ) ( (x,y) \to (6x,7y) ) ( (x,y) \to (x - 6,y - 7) ) ( (x,y) \to (7x,6y) ) ( (x,y) \to (x + 6,y + 7) ) ( (x,y) \to (x + 7,y + 6) ) ( (x,y) \to (x - 7,y - 6) )

Explanation:

Step1: Find the change in \(x\) - coordinate

For point \(D\): \(x\) - coordinate changes from \(2\) to \(-4\). The change is \(-4 - 2=-6\).
For point \(E\): \(x\) - coordinate changes from \(1\) to \(-5\). The change is \(-5 - 1=-6\).
For point \(F\): \(x\) - coordinate changes from \(5\) to \(-1\). The change is \(-1 - 5=-6\).

Step2: Find the change in \(y\) - coordinate

For point \(D\): \(y\) - coordinate changes from \(5\) to \(-2\). The change is \(-2 - 5=-7\).
For point \(E\): \(y\) - coordinate changes from \(8\) to \(1\). The change is \(1 - 8=-7\).
For point \(F\): \(y\) - coordinate changes from \(4\) to \(-3\). The change is \(-3 - 4=-7\).

Answer:

The general rule for the translation is \((x,y)\to(x - 6,y - 7)\)