Since the given rhombus is centered at the origin, S and L are both the same number of units away from the y -axis and F and P are both the same number of units away from the x -axis.
F(0,2b), L(a,0), P(0,- 2b), S(- a,0)
Practice makes perfect
To find the coordinates of the vertices, first notice that the given rhombus is centered at the origin. This tells us that S and L are both the same number of units away from the y -axis. We are given that SL=2a, so both S and L are a units from the y -axis.
2a/2=a
Since L lies on the positive side of the y -axis and S lies on the negative side, their x - coordinates are a and - a. Both points lie on the x -axis, so their y -coordinates are 0.
Once more we will use that the given rhombus is centered at the origin. That tells us that the vertices F and P are both the same number of units away from the x -axis. We are given that FP=4a, so both F and P are the same number of units away from the x -axis.
4b/2=2b
The points lie 2b units away from the x-axis. We know that F lies on the positive side of the x -axis and P lies on the negative side. Therefore, their y - coordinates are 2b and - 2b. Both points lie on the y -axis, so their x -coordinates are 0.
We have now found the coordinates of the vertices and they are F(0,2b), L(a,0), P(0,- 2b), and S(- a,0).
