Question

a mandala is a geometric design that first appeared in india and is now symbolic in many cultures around the world. namrita displays a hand-crafted, wooden mandala, represented by rectangle abcd, on her wall. namrita decides to move the mandala. which transformation could she apply to rectangle abcd to obtain the image rectangle abcd? a 90° counterclockwise rotation around the origin a translation left 10 units a 180° clockwise rotation around the origin a translation left 4 units

Explanation:

Step1: Analyze coordinates (e.g., point A)

Let's take point \( A(1, 2) \) in rectangle \( ABCD \). In \( A'B'C'D' \), the corresponding point \( A' \) should be such that a \( 180^\circ \) rotation around origin \((0,0)\) transforms \((x,y)\) to \((-x,-y)\). For \( A(1,2) \), \( 180^\circ \) rotation gives \((-1,-2)\), which matches \( A' \)'s position (from graph, \( A' \) is at \((-1,-2)\)). Let's check translation: translation left 10 units from \( A(1,2) \) would be \( (1 - 10, 2)=(-9,2) \), not matching. \( 90^\circ \) counterclockwise rotation of \( (1,2) \) is \( (-2,1) \), not matching. Translation left 4 units: \( (1 - 4, 2)=(-3,2) \), not matching.

Step2: Confirm with another point (e.g., B)

Point \( B(1, -2) \) in \( ABCD \). \( 180^\circ \) rotation: \( (-1, 2) \), which matches \( B'(-1,2) \) (from graph). Other transformations: \( 90^\circ \) counterclockwise: \( (2,1) \), no. Translation left 10: \( (1 - 10, -2)=(-9,-2) \), no. Translation left 4: \( (1 - 4, -2)=(-3,-2) \), no.

Answer:

a \( 180^\circ \) clockwise rotation around the origin