Great Math Problem to Challenge yourself

[bjuveges]

Let points and . Quadrilateral is cut into equal area pieces by a line passing through . This line intersects at point , where these fractions are in lowest terms. What is ?

 

[stapel]

Let points and . Quadrilateral is cut into equal area pieces by a line passing through . This line intersects at point , where these fractions are in lowest terms. What is ?

What have you tried? Where are you stuck?

Please be complete. Thank you!

 

[bjuveges]

Already solved it, I just want to form an idea of those that can solve it, hence the poll!

I plotted the points first then drew a line through point A, that intersects Lin CD

Then I used Pick's formula to find the Area, then since the problem says that the shape is cut into equal area pieces I divided the area, 7.5 by 2 to equal 3.25

I found that the bottom half of the shape was a triangle for which I had the base for, so I just solved for the height, which would serve as my Y value

so 3.25=(4(h))/2

Distribute the numbers and I got 7.5/4 so to make it less messy, multiplied it by 2 so 15/8

then I found a equation for the line CD ; if you graph it you realize from point C to D is -3; so I got y=-3x+12 as the line CD i can plug my Y value in for

15/8=-3x+12
15=-24x+96
-81=-24x
27/8=x

so:
(27/8,15/8)

Add the variables up 27+8+15+8=58

I honestly just wanted to see others' insights into the problem and see how many can solve it.

 

[lookagain]

Then I used Pick's formula to find the Area,

then since the problem says that the shape is cut into equal area pieces I divided the area,

7.5 by 2 to equal 3.25 \(\displaystyle \ \ \ \ \ \) <------- That is not correct.

7.5 divided by 2 equals 3.75 instead. However, I didn't read for the correctness of your approach after that.

bjuveges, please have another go at the problem with this different value, please.

 

[bjuveges]

7.5 divided by 2 equals 3.75 instead. However, I didn't read for the correctness of your approach after that.

bjuveges, please have another go at the problem with this different value, please.

my mistake I meant 3.75, drats I always do that!