Question 149699
First plot the two points (0,0) and (3,4). Now draw a right triangle with the hypotenuse that goes through the two points. With the use of pythagoreans theorem, we find that the hypotenuse is 5 units (since {{{sqrt(3^2+4^2)=sqrt(9+16)=sqrt(25)=5}}}). So our drawing looks like this:


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/solution2a7-24-08.png" alt="Photobucket - Video and Image Hosting">


Now if draw the vectors and draw the parallelogram, we can see that the height of the parallelogram is the y-coordinate of the point (3,4). So the first height is 4.


<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/solution2b7-24-08.png" alt="Photobucket - Video and Image Hosting">


So from the drawing, we see that the base is 8 units and the height is 4 units.



Now if we compute the area, we get:


{{{A=b*h=8*4=32}}}



Now let the vector from (0,0) to (3,4) be the new base. So the base is now 5. The area is still 32. So this means that 


{{{32=5h}}}


Solving for h, we get {{{h=32/5=6.4}}}


So the second height is 6.4