sud21 wrote:In xy-plane, a line passed through point (2,2) and divided the quadrilateral formed by (0,0),(7,0),(0,4),(7,4). What is the slope of the line?

Infinite number of slopes are possible unless it is mentioned that the line divides the quadrilateral in two equal parts.

From the question as it is posted, we can only conclude that the line passes through the first quadrant as the quadrilateral is entirely in the first quadrant. There can be infinite number of lines passing through (2, 2) and first quadrant.

BUT if it is mentioned that the line equally divides the quadrilateral, then the line must pass through the center of the quadrilateral, i.e. the point at which the diagonals of the quadrilateral intersects each other.

Center of the quadrilateral = ((0 + 7)/2, (0 + 4)/2) = (3.5, 2)

Hence, the line is passes through (2, 2) and (3.5, 2).
Hence, the slope of the line = (2 - 2)/(3.5 - 0) = 0