help with translate

Question

 

I have a graph with a triangle, A(-1,-2), B(1,2) and C(3,-1).  On the x axis is another A (-4,0).  Also, a line is drawn from D(6,-2) to E(7,-1)

 

 

1.  Help with drawing ΔA'B'C and write a rule to translate ΔA'B'C back to ΔABC

 

2.  Help with drawing the perimage.  The image of (x,y) → (x + 1, y - 5) is D'E'.  (line is drawn over D'E', i couldn't get my computer to draw the line).

 

thanks.

Answer 1

To translate A to A', we have shifted left 3 and up 2. The rule is:

 

(x, y) → (x - 3, y + 2)

 

So, to draw A'B'C', check to make sure the rule works for A and A', then translate B and C:

 

(-1, -2) → (-1 - 3, -2 + 2) → (-4, 0) = A'

(1, 2) → (1 - 3, 2 + 2) → (-2, 4) = B'

(3, -1) → (3 - 3, -1 + 2) → (0, 1) = C'

 

To undo this translation, simply do the opposite. We'll want to shift right 3 and down 2. So:

 

(x, y) → (x + 3, y - 2)

 

 

 

To find the pre-image for D'E', you'll want to undo the translation that's been done to it. Since the original translation is (x, y) → (x + 1, y - 5), you can find DE by applying the rule (x, y) → (x - 1, y + 5) to D'E'. You appear to already have coordinates for D and E, but perhaps you meant to write D' and E'?