Triangle ABC has vertices A(1, 3), B(2, 5), and C(5, 3). What are the coordinates of B' after the translation described by the rule T⟨1, 4⟩ ∘ r(90°, O)?

Answer 1

1) T(1,4) is a translation that adds 1 to every x-coordinate in A, B, and C and 4 to each y-coordinate.

For example:

T(1,4)

(x,y) ----------> (x+1, y+4)

For point A = (1,3):

T(1,4)

(1,3) ---------> (1+1,3+4)

So A' = (2,7)

Do the same for points B and C. The image points after the translation are B' and C'.

2) R(90°,O) is a 90° clockwise rotation of points A', B', and C' about the origin (0,0). The rule for this is:

R(90°,O)

(x,y) -----------> (y,-x)

For A' = (2,7):

R(90°,O)

(2,7) -----------> (7,-2)

So A'', the final image of A after the translation and rotation is A'' = (7,-2)

Do the same for points B' and C' to get B" and C''. A", B'', and C'' are the final answers.