Question

directions: graph and label each figure and its image. give the coordinates of the image.

1. rhombus abcd with vertices a(2, 6), b(6, 7), c(5, 3), and d(1, 2): 180°
2. triangle fgh with vertices f(-7, 8), g(-1, 1), and h(-8, 4): 270° counterclockwise
3. quadrilateral wxyz with vertices w(-6, 7), x(-3, 6), y(-1, 3), and z(-7, 1): 180°

Explanation:

Step1: Recall rotation rules

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

Step2: Solve for rhombus ABCD (180 - degree rotation)

Given $A(2,6)$, then $A'(- 2,-6)$; given $B(6,7)$, then $B'(-6,-7)$; given $C(5,3)$, then $C'(-5,-3)$; given $D(1,2)$, then $D'(-1,-2)$.

Step3: Solve for triangle FGH (270 - degree counter - clockwise rotation)

Given $F(-7,8)$, then $F'(8,7)$; given $G(-1,1)$, then $G'(1,1)$; given $H(-8,4)$, then $H'(4,8)$.

Step4: Solve for quadrilateral WXYZ (180 - degree rotation)

Given $W(-6,7)$, then $W'(6,-7)$; given $X(-3,6)$, then $X'(3,-6)$; given $Y(-1,3)$, then $Y'(1,-3)$; given $Z(-7,1)$, then $Z'(7,-1)$.

Answer:

1. $A'(-2,-6)$, $B'(-6,-7)$, $C'(-5,-3)$, $D'(-1,-2)$
2. $F'(8,7)$, $G'(1,1)$, $H'(4,8)$
3. $W'(6,-7)$, $X'(3,-6)$, $Y'(1,-3)$, $Z'(7,-1)$