Question

draw the reflection of the quadrilateral across the y - axis.

Explanation:

Step1: Identify vertices of quadrilateral

First, find the coordinates of the four vertices of the given quadrilateral. Let's assume the vertices (from the grid) are: \( A(1, 2) \), \( B(6, 1) \), \( C(7, 6) \), \( D(2, 7) \) (by looking at the grid intersections).

Step2: Apply reflection over y - axis rule

The rule for reflecting a point \((x,y)\) over the \(y\) - axis is \((x,y)\to(-x,y)\).

• For point \( A(1, 2) \): After reflection, \( A'(- 1,2) \)
• For point \( B(6, 1) \): After reflection, \( B'(-6,1) \)
• For point \( C(7, 6) \): After reflection, \( C'(-7,6) \)
• For point \( D(2, 7) \): After reflection, \( D'(-2,7) \)

Step3: Plot the reflected points

Plot the points \( A'(-1,2) \), \( B'(-6,1) \), \( C'(-7,6) \), \( D'(-2,7) \) on the grid.

Step4: Connect the reflected points

Connect the points \( A' \), \( B' \), \( C' \), \( D' \) in order to form the reflected quadrilateral.

Answer:

The reflected quadrilateral has vertices at \((-1,2)\), \((-6,1)\), \((-7,6)\), \((-2,7)\) (and is drawn by plotting these points and connecting them).