Question

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?

Answer 1

slope =0

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
`y =2`

Slope of the line =0