sum of coordinates
Points A = ( 3, 9) B = (1 , 1) c = ( 5, 3 ) and D = (a , b) lie in the first quadrant and are the vertices of quadrilateral ABCD. The quadrilateral formed by joining the midpoints of ab, bc, cd, and da is a square. What is the sum of the coordinates of point D?
I solved the problem but someone said that I could've solved it easier and faster by using vectors. I looked up vectors on google and I dont understand it that well. Could someone take a look at my work and show me where i could apply vectors.
Your work is correct
Let I be the midpoint of [AB], J the midpoint of [BC], K the midpoint of [CD] and L the midpoint of [DA]
From the data we have I(2,5) ; J(3,2) ; K((a+5)/2,(b+3)/2) ; L((a+3)/2,(b+9)/2)
[IJ] and [JK] being two sides of a square, they are perpendicular
The dot product of and is equal to 0
The lengths of [IJ] and [JK] are equal
b-1=2 => b=3 => a=7 => D(7,3)
b-1=-2 => b=-1 => a=-5 => D'(-5,-1)
There are 2 solutions depending if you consider ABCD' as a quadrilateral (probably not)
Thanks for your help.
Originally Posted by running-gag
But I think I need to study vectors some more.