Question

plot the image of quadrilateral abcd under a reflection across the y-axis.

Explanation:

Step1: Identify coordinates of ABCD

First, find the coordinates of each vertex of quadrilateral \(ABCD\). From the graph:

• \(A\): Let's assume the coordinates of \(A\) are \((2, -3)\) (by looking at the grid, moving 2 units right on x - axis and 3 units down on y - axis)
• \(B\): Coordinates of \(B\) are \((3, -6)\) (3 units right on x - axis and 6 units down on y - axis)
• \(C\): Coordinates of \(C\) are \((5, -4)\) (5 units right on x - axis and 4 units down on y - axis)
• \(D\): Coordinates of \(D\) are \((4, -2)\) (4 units right on x - axis and 2 units down on y - axis)

Step2: Apply reflection rule over y - axis

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

• For point \(A(2, - 3)\): Applying the rule, the reflected point \(A'\) is \((-2,-3)\)
• For point \(B(3, - 6)\): Applying the rule, the reflected point \(B'\) is \((-3,-6)\)
• For point \(C(5, - 4)\): Applying the rule, the reflected point \(C'\) is \((-5,-4)\)
• For point \(D(4, - 2)\): Applying the rule, the reflected point \(D'\) is \((-4,-2)\)

Step3: Plot the reflected points

Plot the points \(A'(-2,-3)\), \(B'(-3,-6)\), \(C'(-5,-4)\) and \(D'(-4,-2)\) on the coordinate plane and connect them in order to get the reflected quadrilateral.

Answer:

The reflected quadrilateral \(A'B'C'D'\) has vertices at \(A'(-2,-3)\), \(B'(-3,-6)\), \(C'(-5,-4)\) and \(D'(-4,-2)\) (and should be plotted on the coordinate plane by marking these points and connecting them).