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

Answer

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).