Question

determine whether triangle def is a translation of triangle abc. enter the number of the correct statement. statement #1: triangle def is a translation of triangle abc because each point is translated 8 units to the right and 2 units down. statement #2: triangle def is not a translation of triangle abc because the triangles are not congruent. (1 point)

Explanation:

Step1: Identify coordinates of points

Let \(A(-5,5)\), \(B(-5,2)\), \(C(-1,5)\), \(D(3,3)\), \(E(7,3)\), \(F(4,0)\).

Step2: Check translation rule for \(x - coordinate\)

For point \(A(-5)\) to \(D(3)\), the change in \(x\) is \(3-(-5)=8\). For point \(B(-5)\) to \(E(7)\), the change in \(x\) is \(7 - (-5)=8\). For point \(C(-1)\) to \(F(4)\), the change in \(x\) is \(4-(-1)=5\).

Step3: Check translation rule for \(y - coordinate\)

For point \(A(5)\) to \(D(3)\), the change in \(y\) is \(3 - 5=- 2\). For point \(B(2)\) to \(E(3)\), the change in \(y\) is \(3 - 2 = 1\).
Since the \(x\) - coordinate changes are not consistent for all points and \(y\) - coordinate changes are not consistent for all points, the triangles are not related by a single - translation. Also, we can note that translations preserve congruence, but we can directly check the translation rules.

Answer:

Statement #2