Given a triangle ABC where A20 B40 C24 Apply the following t

Given a triangle (ABC), where A=(2,0), B=(4,0), C=(2,4). Apply the following two transformation sequences (a) and (b) to the original triangle ABC individually and generate two new triangles A1B1C1 and A2B2C2. Plot the two new triangles on the figure. (a) T(-1, 0) S (1/2, 1/4) R (90degree) Rf(y,x) (b) R (90degree) T (-1, 0) S (1/2, 1/4) Rf(y, -x)

Solution

(a) On relection around a line y = x, the coordinates ( p, q) change to (q,p) . Therefore, the coordinates of the points A, B and C will change as under:

A: (2,0 ) to (0,2) B: (4,0) to (0,4) C: (2,4) to (4,2)

The next is a rotation counter clockwise by 90⁰. We know that on 90⁰ counter clockwise rotation,   the coordinates of the point (p,q) change to (-q,p). Therefore, the coordinates of the points A, B and C will change as under:

A: (0,2 ) to (-2,0) B: (0,4) to (-4, 0)C: (4,2) to (-2, 4)

The next is translation S (1/2, 1/4). We know that a translation, (h,k) changes the coordinates of the point (p,q) to (p+h, q +k). Therefore, the coordinates of the points A, B and C will change as under:

A: (-2,0 ) to (-3/2, 1/4) B: (-4,0) to (-7/2,1/4)C: (-2,4) to (-3/2,9/4)

The next is translation T (-1, 0). We know that a translation, (h,k) changes the coordinates of the point (p,q) to (p+h, q +k). Therefore, the coordinates of the points A, B and C will change as under:

A: (-3/2, 1/4) to (-5/2, 1/4) B: (-7/2,1/4)to   (-9/2, 1/4)C: (-3/2,9/4)to   (-5/2, 9/4)

(b) On relection around a line y = - x, the coordinates ( p, q) change to (-q,-p) . Therefore, the coordinates of the points A, B and C will change as under:

A: (2,0 ) to (0,-2) B: (4,0) to (0,-4)C: (2,4) to (-4, -2)

The next is translation S (1/2, 1/4). We know that a translation, (h,k) changes the coordinates of the point (p,q) to (p+h, q +k). Therefore, the coordinates of the points A, B and C will change as under:

A: (0,-2) to (1/2, -7/4) B: (0,-4)to (1/2,-15/4)C: (-4,-2)to (-7/2,-7/4)

The next is translation T (-1, 0). We know that a translation, (h,k) changes the coordinates of   the point (p,q) to (p+h, q +k). Therefore, the coordinates of the points A, B and C will change as under:

A: (1/2, -7/4) to (-1/2, -7/4) B: (1/2,-15/4)to (-1/2,-15/4)C: (-7/2,-7/4) to (-9/2,-7/4)

The next is is a rotation counter clockwise by 90⁰. We know that on 90⁰ counter clockwise rotation,   the coordinates of the point (p,q) change to (-q,p). Therefore, the coordinates of the points A, B and C will change as under:

A: (-1/2, -7/4) to (7/4, -1/2) B: (-1/2,-15/4)to (15/4,-1/2)C: (-9/2,-7/4)to (7/4,-9/2)