Drawing points on Argand plane

Question

The points $5 + 5i$, $1− 3i$, $− 4 + 2i$ and $−2 + 6i$ in the Argand plane are:

(a) Collinear

(b) Concyclic

(c) The vertices of a parallelogram

(d) The vertices of a square

So when I drew the diagram, I got an rectangle in the 1st and 2nd quadrant. So, are they vertices of parallelogram? I am not sure!

Zev Chonoles · Accepted Answer · 2013-06-22T18:15:11.357

1

It's not a rectangle, and it's certainly not contained only in the first and second quadrants.

Try plotting the points again.

If you make further efforts on your own and need help, mouse over this box.

enter image description here

Show[ListPlot[{{5, 5}, {1, -3}, {-4, 2}, {-2, 6}},
PlotRange -> {{-7, 7}, {-7, 7}}, AspectRatio -> 1,
PlotStyle -> {Red, PointSize[0.02]}, LabelStyle -> Directive[12]],
Graphics[Text[Style["5+5[ImaginaryI]", Directive[18]], {5, 4.1}]],
Graphics[Text[Style["1-3[ImaginaryI]", Directive[18]], {2.2, -3}]],
Graphics[Text[Style["-4+2[ImaginaryI]", Directive[18]], {-4, 2.7}]],
Graphics[Text[Style["-2+6[ImaginaryI]", Directive[18]], {-3.4, 6}]]]

edited Jun 22 '13 at 18:15

answered Jun 22 '13 at 17:56

Zev Chonoles

129,973

parallelogram ?? – joey rohan Jun 22 '13 at 18:17
Do you see that the points do not form a rectangle? – Zev Chonoles Jun 22 '13 at 18:25
well..may be not..they do? :O – joey rohan Jun 22 '13 at 18:29
I dont see a rec. gosh! am so poor? – joey rohan Jun 22 '13 at 18:33

score 1 · Answer 2 · answered Jun 22 '13 at 18:39

1

Its not collinear, nor a square, nor a parallelogram. Therefore, it must be Concyclic

answered Jun 22 '13 at 18:39

user80551

569

Drawing points on Argand plane

2 Answers2