Part d complete the table to find the rule for the translation, the coordinates of triangle a′b′c′, and the coordinates of the translated image, triangle a″b″c″

original coordinates new coordinates

(x, y) ( , )

a'( , ) a"( , )

b'( , ) b" ( , )

c'( , ) c" ( , )

the general property of translation is as follow:

A translation preserves the length and slope of a line. A translation by a vector of the form V(h, k)shifts the x-coordinate of each point by h units, and the y-coordinate of each point by k units.

so if the triangle ABC is translated to image A′B′C′

we get the new coordinates of B'

A(5, 1)A'(5+x, 1+y), so the vector of translation is V(x, y)

and we know that 6=5+x  and -2=1+y which implies (x, y)=(1,-3)

to find the coordinates of B

B(a, b)B'(a+1, b-3)= (-1,0)

therefore, a+1=-1, and b-3=0 finally  B(-2, 3)

Step-by-step explanation: