Question

rotations
quadrilateral ( afgh ) is rotated ( 90^{circ} ) clockwise about the origin. what will be the coordinates of ( f )?
a. ( f(-1,-3) )
b. ( f(-4,-1) )
c. ( f(1,4) )
d. ( f(4,1) )

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(90^{\circ}\) clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x',y')=(y,-x)\).

Step2: Identify the original coordinates of point \(D\)

From the graph, the coordinates of point \(D\) are \((-1,4)\). Here \(x = - 1\) and \(y = 4\).

Step3: Apply the rotation rule

Using the rule \((x',y')=(y,-x)\), substitute \(x=-1\) and \(y = 4\). Then \(x'=4\) and \(y'=-(-1)=1\).

Answer:

D. \(D'(4,1)\)