Question

take the trapezoid and rotate it 270 degrees counterclockwise around the origin. what are the new coordinates?

Explanation:

First, we need to identify the original coordinates of the trapezoid's vertices. From the graph, let's assume the original coordinates (let's denote the vertices as \( A, B, C, D \)):

• Let's say \( A(-6, 5) \), \( B(-3, 5) \), \( C(-4, 3) \), \( D(-4, 2) \) (we need to confirm the coordinates from the grid; assuming the x - axis and y - axis with grid lines, each grid square is 1 unit. The left - most vertex is at x=-6, y = 5; next at x=-3, y = 5; then at x=-4, y = 3; and the bottom at x=-4, y = 2)

The rule for rotating a point \((x,y)\) 270 degrees counterclockwise around the origin is \((x,y)\to(y, - x)\)

Step 1: Rotate point \( A(-6,5) \)

Using the rule \((x,y)\to(y, - x)\), substitute \( x=-6\) and \( y = 5\)
New coordinates: \( (5,6) \) (since \( y = 5\) and \( -x=-(-6)=6\))

Step 2: Rotate point \( B(-3,5) \)

Using the rule \((x,y)\to(y, - x)\), substitute \( x = - 3\) and \( y=5\)
New coordinates: \( (5,3) \) (since \( y = 5\) and \( -x=-(-3)=3\))

Step 3: Rotate point \( C(-4,3) \)

Using the rule \((x,y)\to(y, - x)\), substitute \( x=-4\) and \( y = 3\)
New coordinates: \( (3,4) \) (since \( y = 3\) and \( -x=-(-4)=4\))

Step 4: Rotate point \( D(-4,2) \)

Using the rule \((x,y)\to(y, - x)\), substitute \( x=-4\) and \( y = 2\)
New coordinates: \( (2,4) \) (since \( y = 2\) and \( -x=-(-4)=4\))

Answer:

If the original vertices are \( A(-6,5) \), \( B(-3,5) \), \( C(-4,3) \), \( D(-4,2) \), the new coordinates after 270 - degree counterclockwise rotation are \( (5,6) \), \( (5,3) \), \( (3,4) \), \( (2,4) \) (Note: The answer depends on the accurate original coordinates. If the original coordinates are different, the rotated coordinates will change accordingly. The key is to apply the rotation rule \((x,y)\to(y, - x)\) for 270 - degree counterclockwise rotation about the origin)