Is this the right way to find the co-ordinates?

Question

Is this right? Or is there a better way to find co-ordinates? It was the only way I could think of to do it, since it has to form a square, ABCD.

http://s221.photobucket.com/albums/dd223/azuradragonfly/?action=view¤t=maths1.jpg

Answer 1

Hi,

Your coordinates are correct, but it forms a rectangle instead of a square. I hope that helps!! :-)

Answer 2

The way you find the missing co-ordinates of a square given two diagonal corners is to recall that the diagonals of a square must be perpendicular bisectors of each other.

Graphically, you connect the points and erect the perpendicular bisector to the line using compass and straight-edge. Then, using the compass and with the intersection of the bisectors as center and the half-length of the original line as radius, strike off arcs on the bisector. the intersection of these arcs and the bisector are then the missing points, B & D.

Analitically, proceed as follows:
A = (7, 2)
C = (1, 4)
O = ((7 + 1)/2, (4 + 2)/2) = (4, 3) (center)
m1 = (2 - 4) / (7 - 1) = - 1/3 (slope of CA)
m2 = (-1) / (- 2/3) = 3/1 (slope of BD)
B = (4 - 1 , 3 - 3) = (3, 0)
D = (4 + 1, 3 + 3) = (5, 6)

With this data you can graph the square or, using point-slope method determine the equations of all the lines involved.

The length of the sides of the square is
√((7 - 3)^2 + (2 - 0)^2) = √(16 + 4) = √20 = 2√5

Answer 3

no you made a rectangle!
The only possible square has the points
A(7,2)
B(3,0)
C(1,4)
D(5,6) with a mid point M(4,3)
M is the difference between C and A (subtract x's and y's)
Draw these 3 points A,C, M and the other 2 (B,D) are easy enough to see (use gridded graph paper or a suitable program)