We should now translate the rectangle to get the image Q'R'S'T'. The preimage QRST should be translated left 3 units and down 3 units.
Translation: (x,y) → (x-3,y-3)
Let's now use the translation rule to calculate the image of each of the vertices Q, R, S, and T.
Translation
Simplify
Q(2,- 3) → Q'(2-3,- 3-3)
Q(2,- 3) → Q'(- 1,- 6)
R(2,4) → R'(2-3,4-3)
R(2,4) → R'(- 1,1)
S(5,4) → S'(5-3,4-3)
S(5,4) → S'(2,1)
T(5,- 3) → T'(5-3,- 3-3)
T(5,- 3) → T'(2,- 6)
Now that we calculated the coordinates of Q' R', S', and T', we can plot them and draw rectangle Q'R'S'T'.
We see above that both rectangles have the same base 3 and the same height 7. Let's calculate both areas.
Area ofQRST:& 7 * 3 = 21
Area ofQ'R'S'T':& 7 * 3 = 21
The area of both QRST and Q'R'S'T' is 21 square units.
b
From Part A we know that the area of both QRST and Q'R'S'T' is 21 square units. Therefore, despite the fact that the preimage and image have different positions, QRST and Q'R'S'T' have the same area. We can conclude that a translation does not affect the area.
