Question

rotate the figure the given number of degrees about the origin. list the coordinates of the vertices of the image.
rotate 270°
a (, )
b (, )
c (, )
d (, )

Explanation:

Step1: Determine the rotation rule

When rotating a point \((x,y)\) \(270^{\circ}\) counter - clockwise about the origin, the rule is \((x,y)\to(y, - x)\).

Step2: Find the coordinates of the original points

From the graph, \(A(-1,1)\), \(B(0,3)\), \(C(4,3)\), \(D(3,1)\).

Step3: Apply the rotation rule to each point

• For point \(A(-1,1)\):

Substitute \(x=-1\) and \(y = 1\) into the rule \((x,y)\to(y,-x)\). We get \(A'(1,1)\).

• For point \(B(0,3)\):

Substitute \(x = 0\) and \(y=3\) into the rule \((x,y)\to(y,-x)\). We get \(B'(3,0)\).

• For point \(C(4,3)\):

Substitute \(x = 4\) and \(y = 3\) into the rule \((x,y)\to(y,-x)\). We get \(C'(3,-4)\).

• For point \(D(3,1)\):

Substitute \(x=3\) and \(y = 1\) into the rule \((x,y)\to(y,-x)\). We get \(D'(1,-3)\).

Answer:

\(A'(1,1)\), \(B'(3,0)\), \(C'(3,-4)\), \(D'(1,-3)\)