A triangle has vertices at the points
A(−6, 9), B(6, 3) and C(9,−6).
Suppose that the triangle is to be moved so that
B is at the origin
BC lies along the positive x-axis. One isometry that achieves this
transformation is the composite of a translation followed by a
rotation. (You may find it helpful to sketch the triangle.)
(i) Determine the translation that moves
B to the origin, giving your
answer in the form
ta,b. Write down a formal definition of this
translation in two-line notation.
(ii) Find the coordinates of the images
A! of A and C! of C under the
translation in part (a)(i).
rθ be the rotation that completes the required
θ lies in the interval (−π, π]. Find the
exact values of tan
θ, cos θ and sin θ, and hence write down a
formal definition of
rθ using two-line notation. (There is no need
to work out the value of the angle
(iv) Find the coordinates of the images of
A! and C! under the
rθ. Give your answers as exact values.
(v) Write down a formal definition of the composite transformation,
that is, the result of the translation in part (a)(i) followed by the
rotation in part (a)(iii).
I've been stuck on this all day! I have t-6,3 for part (i) and found A to be (-12,6) and C to be (3,-9) for part (ii).
Other than that I'm totally lost!
Any help would be really appreciated, thanks.