Question

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?

Answer 1

sketch graph
from y = -8 must go down 4
so at y = -12
from x = 0 must go right 7
so at x = 7
so
(7,-12)

Answer 2

Credit goes to damon: http://www.jiskha.com/display.cgi?id=1326927624

Answer 3

http://openstudy.com/users/jewjewbri#/updates/4fc944d7e4b0c6963ad3a374

gotta start reading a new book :/

Answer 4

First, find the slope of the diagonal which is 1/2.
Then find the slope of a segment that is perpendicular to this one which is -2.
Then find the midpoint of the diagonal which is (4, -6).
Then find the distance between the midpoint and the third vertex which is 3√5.
Then plug that into the distance formula.
3√5 = √((x - 4)^2 + (y + 6)^2)
45 = ((x - 4)^2 + (y + 6)^2)
45 = x^2 - 8x + 16 + y^2 + 12y + 36
45 = x^2 - 8x + y^2 + 12y + 52
Then plug it back into the slope formula.
-2 = (-6 - y)/(4 - x)
-8 + 2x = -6 - y
y = 2 - 2x
Then plug this into the distance formula.
45 = x^2 - 8x + y^2 + 12y + 52
0 = x^2 - 8x + y^2 + 12y + 7
0 = x^2 - 8x + (2 - 2x)^2 + 12(2 - 2x) + 7
0 = x^2 - 8x + 4x^2 - 8x + 4 + 24 - 24x + 7
0 = 5x^2 - 40x + 35
0 = (5x - 5)(x - 7)
x = 1 or 7 which is 7 using logic.
Plug it back in.
y = 2 - 2(7)
y = -12
(7, -12)
Convoluted way for the win!!!! I guess you could just graph it. :)

Answer 5

whatever gets you thru the night :)

Answer 6

lol ^_^