Answer: The image of triangle DEF is triangle GHJ.
Step-by-step explanation: We are given to find he image of triangle DEF under the following translation :
(x, y) ⇒ (x + 7, y + 2).
From the graph, we notice that
the co-ordinates of the vertices of triangle DEF are D(-5, 1), E(-2, 4) and F(-2, 1).
Also, the co-ordinates of the vertices of the optional triangles are :
ABC : A(-7, 4), B(-4, 7) and C(-4, 4)
GHJ : G(2, 3), H(5, 6) and J(5, 3)
KLM : K(1, -5), L(4, -2) and M(4, -5)
NPQ : N(-7, -6), P(-4, -3) and Q(-4, -6).
Now, after the translation (x, y) ⇒ (x + 7, y + 2), the co-ordinates of the vertices of triangle DEF becomes :
D(-5, 1) ⇒ (-5+7, 1+2) = (2, 3),
E(-2, 4) ⇒ (-2+7, 4+2) = (5, 6),
F(-2, 1) ⇒ (-2+7, 1+2) = (5, 3).
We see that the transformed co-ordinates ae the co-ordinates of the vertices of triangle GHJ.
Thus, the required image of triangle DEF is triangle GHJ.