Question

Three of the vertices of a quadrilateral region are, in order, (1,1), (2,7), and (5,7). If the area of the enclosed region is 14, and all coordinates have integer values, in how many possible positions could the fourth vertex be?

Answer 1

Anyone familiar with the shoelace method? That's apparently what they did, but I don't know what it is.

Answer 2

never heard of showlace method..

im still working on the problem...
is the answer infiniti ?

Answer 3

I've never used the shoelace method either, but wikipedia has some good information on it. Give me a couple more minutes to see if I can use it to get an answer. http://en.wikipedia.org/wiki/Shoelace_formula

Answer 4

Yeah. Turns out it is infinity. This is their explanation:
Can someone maybe explain it to me?

Answer 5

i worked out similar way :
1) area of triangle formed by 3 given points = 9 sq.units
2) area of triangle formed by fourth point = 5 sq.units

now i got the equation as :
y = (3/2)x -2

this has same slope as its base.. so there will be infiniti possible points.
ill post a diagram..

Answer 6

Maybe the shoelace method is similar to the method of going clockwise or counterclockwise using points of a triangle to find the area?

Answer 7

I see why it's called the shoelace method now. Basically what they're doing, is multiplying things in a certain way. Hold on one second to to see if I can show it in a simple way.