Question

rotate point b 90° clockwise around the origin. in which quadrant is point b? quadrant iv rotate point c 90° counterclockwise around the origin.

Explanation:

Step1: Determine the coordinates of point \( B \)

From the graph, assume the coordinates of point \( B \) are \( (1,2) \).
The rule for a \( 90^{\circ} \) clockwise rotation about the origin \((x,y)\to(y, -x)\).
Substituting \( x = 1,y = 2 \) into the formula: \( (1,2)\to(2,-1) \).

Step2: Determine the quadrant of \( B' \)

In the coordinate system, for a point \( (x,y) \), if \( x>0 \) and \( y < 0 \), the point is in Quadrant IV.
Since for \( B'(2,-1) \), \( x = 2>0 \) and \( y=-1 < 0 \), it is in Quadrant IV.

Step3: Determine the coordinates of point \( C \)

From the graph, assume the coordinates of point \( C \) are \( (1,4) \).
The rule for a \( 90^{\circ} \) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\).
Substituting \( x = 1,y = 4 \) into the formula: \( (1,4)\to(-4,1) \).

Answer:

• For the rotation of point \( B \): The quadrant of \( B' \) is Quadrant IV.
• For the rotation of point \( C \): If the original coordinates of \( C \) are \((1,4)\), after a \( 90^{\circ} \) counter - clockwise rotation about the origin, the new coordinates are \((-4,1)\).