Question

WORTH 20 POINTS!!

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? (7, -12)
(7, -8)
(-8, -4)
(-4, -12)

Answer 1

Think about this problem as follows:

The rhombus consists of two lines which connecting the endpoints which are intersecting each other. If you have the slopes of these, you can create a relation which says that

`k_1 \cdot k_2 = -1`
where
`k_i` are the slopes of the lines.

Now you have one slope, which is
`k_1 = (-8 - (-4))/(0-8) = (1)/(2)` which means that the slope of the other one has to be


`k_2 = -1 \cdot 2 = -2`

Given that you have the point (1,0) its trivial to see that this is satisfied by the point (7,-12)
`k_2 = (-12-0)/(7-1)=(-12)/(6) = -2`

Its worth noting that you want to draw the points, that you have the correct order when you calculate the slope.