Question

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. fill in the blank 2 points a. a (_, _) b (_, _) c (_, _) fill in the blank 2 points b. d (_, _) e (_, _) f (_, _) g (_, _)

Explanation:

Step1: Recall translation rule for horizontal shift

For a horizontal translation of \(h\) units, if \(h>0\) the point moves right and if \(h < 0\) the point moves left. The rule for a horizontal translation of \(h\) units for a point \((x,y)\) is \((x + h,y)\).

Step2: Translate triangle ABC

Given \(h=- 4\) (4 units to the left). For point \(A(2,4)\), the new - \(x\) coordinate is \(2+( - 4)=-2\) and the \(y\) - coordinate remains the same. So \(A'(-2,4)\). For point \(B(3,6)\), the new \(x\) - coordinate is \(3+( - 4)=-1\) and the \(y\) - coordinate remains the same. So \(B'(-1,6)\). For point \(C(5,1)\), the new \(x\) - coordinate is \(5+( - 4)=1\) and the \(y\) - coordinate remains the same. So \(C'(1,1)\).

Step3: Translate parallelogram DEFG

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

Answer:

For triangle ABC: \(A'(-2,4)\), \(B'(-1,6)\), \(C'(1,1)\)
For parallelogram DEFG: \(D'(-7,2)\), \(E'(-6,5)\), \(F'(-1,5)\), \(G'(-2,2)\)