Question

translations
determine the coordinates of the image following each given translation.
① triangle abc with coordinates a(2, 4), b(3, 6), and c(5, 1) is translated 4 units horizontally.
② parallelogram defg with coordinates d(0, 2), e(1, 5), f(6, 5), and g(5, 2) is translated - 7 units horizontally.

Explanation:

Step1: Recall translation rule for horizontal shift

For a horizontal translation \(h\) units to the right (if \(h>0\)) or left (if \(h < 0\)) of a point \((x,y)\), the new - point is \((x + h,y)\).

Step2: Translate triangle ABC 4 units horizontally

For point \(A(2,4)\), the new \(x\) - coordinate is \(2 + 4=6\) and \(y\) - coordinate remains \(4\). So the new point \(A'\) is \((6,4)\).
For point \(B(3,6)\), the new \(x\) - coordinate is \(3 + 4 = 7\) and \(y\) - coordinate remains \(6\). So the new point \(B'\) is \((7,6)\).
For point \(C(5,1)\), the new \(x\) - coordinate is \(5+4 = 9\) and \(y\) - coordinate remains \(1\). So the new point \(C'\) is \((9,1)\).

Step3: Translate parallelogram DEFG - 7 units horizontally

For point \(D(0,2)\), the new \(x\) - coordinate is \(0+( - 7)=-7\) and \(y\) - coordinate remains \(2\). So the new point \(D'\) is \((-7,2)\).
For point \(E(1,5)\), the new \(x\) - coordinate is \(1+( - 7)=-6\) and \(y\) - coordinate remains \(5\). So the new point \(E'\) is \((-6,5)\).
For point \(F(6,5)\), the new \(x\) - coordinate is \(6+( - 7)=-1\) and \(y\) - coordinate remains \(5\). So the new point \(F'\) is \((-1,5)\).
For point \(G(5,2)\), the new \(x\) - coordinate is \(5+( - 7)=-2\) and \(y\) - coordinate remains \(2\). So the new point \(G'\) is \((-2,2)\).

Answer:

Coordinates of the translated triangle \(A'(6,4)\), \(B'(7,6)\), \(C'(9,1)\); coordinates of the translated parallelogram \(D'(-7,2)\), \(E'(-6,5)\), \(F'(-1,5)\), \(G'(-2,2)\)