Question #936dc

1 Answer
Srinivas · mimi
Oct 5, 2015

#(-3,-6)# and #(-6,8)#

Explanation:

Let the co-ordinates of one vertex be #(x_1, y_1)# and the other vertex be #(x_2,y_2)#.

The diagonals meet at the midpoint of each diagonal.
The co-ordinates of the midpoint are the average of the two end points.

This means that you can find the co-ordinates of the midpoint by adding the #x# co-ordinates of the opposite vertices and dividing the sum by #2# to get the #x# co-ordinate, and by adding the #y# co-ordinates of the same vertices and dividing the sum by #2# to get the #y# co-ordinate.

#(x_1+7)/2=2#

#x_1=-3#

And

#(y1+16)/2=5#

#y_1=-6#

So the first set of co-ordinates is #(-3,-6)#.

#(x_2+10)/2=2#

#x_2=-6#

And

#(y_2+2)/2=5#

#y_2=8#

So the second set of co-ordinates is #(-6,8)#

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