Question

Triangle RST has vertices R(2, 0), S(4, 0), and T(1, –3). The image of triangle RST after a rotation has vertices R'(0, –2), S'(0, –4), and T'(–3, –1). Which rule describes the transformation?\

Answer 1

Answer with explanation:

Pre -image= Vertices of Δ R ST=R(2, 0), S(4, 0), and T(1, –3)

Image of Δ R ST after rotation= R'(0, –2), S'(0, –4), and T'(–3, –1)

Pre-Image lies in Fourth Quadrant and Image lies in Third Quadrant.

If triangle is rotated by different angles in anticlockwise direction,then

   $(a,b)_{90^{\circ}}=(-b, a)\\\\(a,b)_{180^{\circ}}=(-b, -a)\\\\(a,b)_{270^{\circ}}=(b, -a)$

If triangle is rotated by different angles in Clockwise direction,then

     $(a,b)_{90^{\circ}}=(b, -a)\\\\(a,b)_{180^{\circ}}=(-b, -a)\\\\(a,b)_{270^{\circ}}=(-b, a)$

⇒→So, Pre image that is ,Δ R ST having vertices ,R(2, 0), S(4, 0), and T(1, –3) when rotated by either 90° in clockwise direction or by 270°, in anticlockwise Direction to get Image Δ R' S'T' having vertices R'(0, –2), S'(0, –4), and T'(–3, –1)  .