Question

drag the tiles to the boxes to form correct pairs.

polygon (abcd) is rotated (90^circ) counterclockwise about the origin to create polygon (abcd). match each set of coordinates to the vertices of polygon (abcd).

Explanation:

Identify the original coordinates

Using Coordinate Geometry, we read the coordinates of the vertices of polygon \(ABCD\) from the graph:

• \(A = (1, 1)\)
• \(B = (1, 2)\)
• \(C = (2, 2)\)
• \(D = (3, 1)\)

Apply the rotation rule

A counterclockwise rotation of \(90^\circ\) about the origin maps any point \((x, y)\) to \((-y, x)\).

Calculate the image coordinates

Applying the rule \((x, y)
ightarrow (-y, x)\) to each vertex:

• For \(A(1, 1)\):

$$ A' = (-1, 1) $$

• For \(B(1, 2)\):

$$ B' = (-2, 1) $$

• For \(C(2, 2)\):

$$ C' = (-2, 2) $$

• For \(D(3, 1)\):

$$ D' = (-1, 3) $$

Match the pairs

We pair each transformed vertex with its corresponding coordinate:

• \(A'\) matches with \((-1, 1)\)
• \(B'\) matches with \((-2, 1)\)
• \(C'\) matches with \((-2, 2)\)
• \(D'\) matches with \((-1, 3)\)

Answer:

Vertex	Coordinate
\(B'\)	\((-2, 1)\)
\(C'\)	\((-2, 2)\)
\(D'\)	\((-1, 3)\)