Question

rotate the figure the given number of degrees about the origin. list the coordinates of the vertices of the image.
rotate 180°
a(
,
)
b(
,
)
c(
,
)
d(
,
)

Explanation:

Step1: Find original coordinates

From the graph, \(A(-1,0)\), \(B(-2,2)\), \(C(-1,4)\), \(D(0,2)\)

Step2: Apply 180 - degree rotation formula

The formula for a \(180^{\circ}\) rotation about the origin is \((x,y)\to(-x,-y)\)
For point \(A(-1,0)\):
\(x=-1,y = 0\), after rotation \(A'=(1,0)\)
For point \(B(-2,2)\):
\(x=-2,y = 2\), after rotation \(B'=(2,-2)\)
For point \(C(-1,4)\):
\(x=-1,y = 4\), after rotation \(C'=(1,-4)\)
For point \(D(0,2)\):
\(x = 0,y=2\), after rotation \(D'=(0,-2)\)

Answer:

\(A'(1,0)\), \(B'(2,-2)\), \(C'(1,-4)\), \(D'(0,-2)\)