Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.
quadrilateral qrst is reflected across the y - axis and rotated 360° clockwise about the origin to create the quadrilateral qrst. what are the vertex coordinates of quadrilateral qrst?
graph of a coordinate plane with quadrilateral qrst plotted. tiles with coordinates: (-5, -2), (1, -4), (-4, -6), (-1, 4), (-2, -1), (5, 2)

Explanation:

Step1: Identify original coordinates

First, we find the coordinates of the original quadrilateral QRST from the graph. Let's assume the coordinates are:

• \( Q(-1, -4) \)
• \( R(2, -1) \)
• \( S(5, -2) \)
• \( T(4, -6) \) (Wait, looking at the graph again, let's correct. From the graph, let's re - identify:

Looking at the points:

• \( Q \): Let's see, the x - coordinate is - 1, y - coordinate is - 4? Wait, no, the blue points: Wait, the original points: Let's check the graph. The point \( R \) is at (2, - 1), \( S \) is at (5, - 2), \( T \) is at (4, - 6), and \( Q \) is at (- 1, - 4)? Wait, maybe I misread. Wait, the tiles are given as (- 5, - 2), (1, - 4), (- 4, - 6), (- 1, 4), (- 2, - 1), (5, 2). Wait, maybe the original coordinates are:

Let's re - examine the graph:

• \( Q \): Let's say \( Q(-1, - 4) \)
• \( R(2, - 1) \)
• \( S(5, - 2) \)
• \( T(4, - 6) \)

Step2: Reflect across the y - axis

The rule for reflection across the y - axis is \((x,y)\to(-x,y)\).

• For \( Q(-1, - 4) \): After reflection, \( Q_1(1, - 4) \)
• For \( R(2, - 1) \): After reflection, \( R_1(-2, - 1) \)
• For \( S(5, - 2) \): After reflection, \( S_1(-5, - 2) \)
• For \( T(4, - 6) \): After reflection, \( T_1(-4, - 6) \)

Step3: Rotate \( 360^\circ \) clockwise

A \( 360^\circ \) rotation about the origin (clockwise or counter - clockwise) leaves the coordinates unchanged. The rule for a \( 360^\circ \) rotation is \((x,y)\to(x,y)\). So the coordinates after reflection and then \( 360^\circ \) rotation are the same as after reflection.

So the coordinates of \( Q'R'S'T' \) are:

• \( Q'(1, - 4) \)
• \( R'(-2, - 1) \)
• \( S'(-5, - 2) \)
• \( T'(-4, - 6) \)

Answer:

The vertex coordinates of quadrilateral \( Q'R'S'T' \) are \( Q'(1, - 4) \), \( R'(-2, - 1) \), \( S'(-5, - 2) \), \( T'(-4, - 6) \)