The vertices of a rectangle in the standard (x, y) coordinate plane are (0,0), (0,4), (7,0), and (7,4). if a line through (2,2) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?

slope =0

Step-by-step explanation:

Given that the vertices of a rectangle in the standard (x,y) coordinate plane are (0,0), (0,4), (7,0), and (7,4).

The rectangle has length = 7 and width =4

We know rectangle has two lines of symmetry which are i) vertical line through mid point ii) Horizontal line through mid point

Since the line passes through (2,2) we have the line as middle line.

Hence the required line is

Slope of the line =0

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.