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)
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 [tex]k_1 \cdot k_2 = -1[/tex] where [tex]k_i[/tex] are the slopes of the lines.
Now you have one slope, which is [tex]k_1 = \frac{-8 - (-4)}{0-8} = \frac{1}{2}[/tex] which means that the slope of the other one has to be
[tex]k_2 = -1 \cdot 2 = -2[/tex]
Given that you have the point (1,0) its trivial to see that this is satisfied by the point (7,-12)[tex]k_2 = \frac{-12-0}{7-1}=\frac{-12}{6} = -2[/tex]
Its worth noting that you want to draw the points, that you have the correct order when you calculate the slope.
