Question

triangle abc is translated 8 units to the right and 7 units up. the result is △abc, as shown below. (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 ( a(-8,-8) \to a(square,square) ) ( b(-7,-5) \to b(square,square) ) ( c(-3,-7) \to c(square,square) ) (b) choose the general rule below that describes the translation mapping ( \triangle abc ) to ( \triangle abc ). ( (x,y) \to (8x,7y) ) ( (x,y) \to (x + 8,y + 7) ) ( (x,y) \to (-8x,-7y) ) ( (x,y) \to (-7x,-8y) ) ( (x,y) \to (x - 8,y - 7) ) ( (x,y) \to (7x,8y) ) ( (x,y) \to (x - 7,y - 8) ) ( (x,y) \to (x + 7,y + 8) )

Explanation:

Step1: Calculate \(A'\) coordinates

For a translation \(8\) units right (\(x\)-coordinate \(+ 8\)) and \(7\) units up (\(y\)-coordinate \(+7\)).
For \(A(-8,-8)\), \(x=-8 + 8=0\), \(y=-8 + 7=-1\).

Step2: Calculate \(B'\) coordinates

For \(B(-7,-5)\), \(x=-7 + 8 = 1\), \(y=-5+7 = 2\).

Step3: Calculate \(C'\) coordinates

For \(C(-3,-7)\), \(x=-3 + 8=5\), \(y=-7 + 7=0\).

Step4: Determine the general rule

The general rule for a translation of \(h = 8\) (right) and \(k = 7\) (up) is \((x,y)\to(x + h,y + k)=(x + 8,y + 7)\).

Answer:

(a) \(A'(\boldsymbol{0},\boldsymbol{-1})\), \(B'(\boldsymbol{1},\boldsymbol{2})\), \(C'(\boldsymbol{5},\boldsymbol{0})\)
(b) \((x,y)\to(x + 8,y + 7)\)