The endpoints of one diagonal of a rhombus are (0, -8) and (8, -4). If the coordinates of the 3rd vertex are (1, 0), what are the coordinates of the 4th vertex?

Question

amistre64 · Answer

id say we can find the midpoint and use that to our advantage

anonymous · Answer

how would we do that?

amistre64 · Answer

whats the middle between 0 and 8 ?

anonymous · Answer

-4?

amistre64 · Answer

i dont believe there are any negative numbers between 0 and 8; but I would go with 4 :)

amistre64 · Answer

whats the middle between -8 and -4?

anonymous · Answer

Oh haha you're right. not sure? -6?

amistre64 · Answer

correct.  ideally, we add the endpoints and divide it in half to get the mid point 

(0,-8)
(8,-4)
------
(8,-12)/2 ; (4,-6)

amistre64 · Answer

now we know the center of the thing, and that has to be in the center of the other vertexes right?

anonymous · Answer

Oh ok, and yeah

amistre64 · Answer

(1,0)
(x, y)
-----
(x+1, y+0) /2 = (4,-6)

therefore

(x+1)/2 = 4

(y+0)/2 = -6

solve for x and y

anonymous · Answer

x=4 y=-6?

amistre64 · Answer

um, not quite

amistre64 · Answer

(x+1)/2 = 4 , *2

x+1 = 8
   -1   -1
--------
x     = 7

(y+0)/2 = -6 , *2

y+0 = -12

y = -12

anonymous · Answer

oh! so then x=-4?

anonymous · Answer

nvm haha 7!

amistre64 · Answer

the magic 8ball says 7 lol

anonymous · Answer

haha so I saw. well I thank you for the help :)

amistre64 · Answer

youre welcome, and good luck ;)

anonymous · Answer

Thank You