A rectangle is plotted in the coordinate plane. The vertices (corners) of the rectangle are given as A(–2,3), B(4,3); C(–2, –2) and D(x,y). What is the ordered pair for point D?
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A(-2,3),--B(4,3)
C(-2,-2), D(4,y)
AC = -2-3 = -5
BD = AC = -5 = y-3
y-3 = -5
Y = -2.
so big
To find the coordinates of point D, we can use the properties of rectangles.
In a rectangle, opposite sides are parallel and equal in length. Additionally, the diagonals of a rectangle bisect each other.
Given that point A is (-2,3) and point C is (-2,-2), we know that these two points determine the height of the rectangle.
The height of the rectangle is the vertical distance between A and C, so we can calculate it as follows:
Height = y-coordinate of C - y-coordinate of A
= -2 - 3
= -5
Now, since opposite sides of a rectangle are parallel, we can conclude that the line segment joining A and B is parallel to the line segment joining C and D.
Since the y-coordinate of A and B are the same (3), the y-coordinate of D should also be the same.
So, the y-coordinate of point D is 3.
Now, to find the x-coordinate of point D, we can use the fact that the diagonals of a rectangle bisect each other.
Since diagonal AC bisects diagonal BD, the x-coordinate of D should be the same as the x-coordinate of point C.
Therefore, the x-coordinate of point D is -2.
Combining the x and y coordinates, the ordered pair for point D is (-2, 3).