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
[tex](a,b)_{90^{\circ}}=(-b, a)\\\\(a,b)_{180^{\circ}}=(-b, -a)\\\\(a,b)_{270^{\circ}}=(b, -a)[/tex]
If triangle is rotated by different angles in Clockwise direction,then
[tex](a,b)_{90^{\circ}}=(b, -a)\\\\(a,b)_{180^{\circ}}=(-b, -a)\\\\(a,b)_{270^{\circ}}=(-b, a)[/tex]
⇒→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) .
