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Question

A(-1,-1), B(6,1), C(8,8), D(x,y) are the four vertices of a rhombus taken in order. Find the co-ordinates of point D.

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Solution

AB=(6+D2)+(1+D2)AD=(x+1)2(y+1)2=4a+4=x2+2x+1+y2+2y+1=51=x2+y2+2x+2y+2
DC=(x+8)2+(y+8)2BC=(86)2(81)2=x216x+64+y216y+64=4+49=x2+y216x16y+128=53
AB =AD & BC =DC

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