Question

rotating a figure the coordinates of the vertices of a figure are given. rotate the figure as described.

1. a(2, -2), b(4, -1), c(4, -3), d(2, -4)

90° counterclockwise about the origin

1. f(1, 2), g(3, 5), h(3, 2)

180° about the origin

1. j(-4, 1), k(-2, 1), l(-4, -3)

90° clockwise about the origin

1. p(-3, 4), q(-1, 4), r(-2, 1), s(-4, 1)

270° clockwise about the origin

1. m(-6, -2), x(-2, -2), y(-2, -6), z(-5, -6)

270° counterclockwise about the origin

1. a(1, -1), b(5, -6), c(1, -6)

90° counterclockwise about the origin

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation about the origin \((x,y)\to(-y,x)\). For a 180 - degree rotation about the origin \((x,y)\to(-x,-y)\). For a 270 - degree counter - clockwise (which is equivalent to 90 - degree clockwise) rotation about the origin \((x,y)\to(y, - x)\).

Step2: Apply rules to 13

For point A(2, - 2), using \((x,y)\to(-y,x)\), we get A'(-(-2),2)=(2,2). For B(4, - 1), B'(-(-1),4)=(1,4). For C(4, - 3), C'(-(-3),4)=(3, - 4). For D(2, - 4), D'(-(-4),2)=(4,2).

Step3: Apply rules to 14

For a 180 - degree rotation, for point F(1,2), F'(-1,-2). For G(3,5), G'(-3,-5). For H(3,2), H'(-3,-2).

Step4: Apply rules to 15

For a 90 - degree clockwise rotation (270 - degree counter - clockwise), for J(-4,1), J'(1, - 4). For K(-2,1), K'(1, - 2). For L(-4,3), L'(3, - 4).

Step5: Apply rules to 16

For a 270 - degree counter - clockwise rotation, for P(-3,4), P'(4,3). For Q(-1,4), Q'(4,1). For R(-2,1), R'(1,2). For S(-4,1), S'(1,4).

Step6: Apply rules to 17

For a 270 - degree counter - clockwise rotation, for W(-6, - 2), W'( - 2, - 6). For X(-2, - 2), X'( - 2, - 2). For Y(-2, - 6), Y'( - 6, - 2). For Z(-5, - 6), Z'( - 6, - 5).

Step7: Apply rules to 18

For a 90 - degree counter - clockwise rotation, for A(-1,1), A'(1,1). For B(5, - 6), B'(6,5). For C(1, - 6), C'(6,1).

Answer:

1. A'(- 2,2), B'(1,4), C'(3, - 4), D'(4,2)
2. F'(-2, - 2), G'(-3, - 5), H'(-3, - 2)
3. J'(1, - 4), K'(2, - 1), L'(4, - 3)
4. P'(4,3), Q'(4,1), R'(1,2), S'(1,4)
5. W'(2, - 6), X'(2, - 2), Y'(6, - 2), Z'(6, - 5)
6. A'(1,1), B'(6,5), C'(6,1)