Question

You are given the coordinates of a triangle and coordinates for only one of the vertices of its image under a translation. Explain how to translate the entire triangle.

Answer 1

By adding them together

Answer 2

1. Let A(a,b), B(c,d), C(e,f) be the three vertices of the triangle ABC, with coordinates as given.

2. Let A'(m,n) be the coordinate of vertex A under the translation.

    A translation is the shifting of a figure only horizontally(left or right) and vertically (up or down).

So assume that the translation is + t horizontally, +k vertically (bot t and k can be negative, so in that case +t would mean shifting left, + k shifting down)

3. 

A is translated to A' t units horizontally, k vertically means that
   a+t=m
   b+k=n

so t=m-a
     k=n-b

t and k are no more unknowns since a, b, m, n we assumed known values.

The translation of point B is B' with coordinates (b+t, c+k) and of C is C' (e+t, f+k)

Now join A', B' and C' to each other.