Question

quadrilateral pqrs is rotated 90° clockwise about the origin to form quadrilateral pqrs. what is the y - coordinate of point p?

Explanation:

1. Recall the rule for a 90 - degree clock - wise rotation about the origin:

• The rule for rotating a point \((x,y)\) 90 degrees clock - wise about the origin is \((x,y)\to(y, - x)\).

1. Identify the coordinates of point \(P\):

• By observing the graph, the coordinates of point \(P\) are \((0,3)\).

1. Apply the rotation rule to point \(P\):

• Using the rule \((x,y)\to(y, - x)\), when \(x = 0\) and \(y = 3\), we substitute these values into the rule.
• For point \(P(0,3)\), after rotation, the new coordinates \(P'\) are \((3,0)\).

1. Determine the \(y\) - coordinate of \(P'\):

• The coordinates of \(P'\) are \((3,0)\), so the \(y\) - coordinate of \(P'\) is \(0\).

Step 1: Recall rotation rule

The rule for 90 - degree clock - wise rotation about origin is \((x,y)\to(y, - x)\).

Step 2: Identify \(P\) coordinates

Point \(P\) has coordinates \((0,3)\).

Step 3: Apply rotation rule

Substitute \(x = 0\) and \(y = 3\) into \((x,y)\to(y, - x)\) to get \((3,0)\).

Step 4: Find \(y\) - coordinate

The \(y\) - coordinate of \((3,0)\) is \(0\).

Answer:

\(0\)