can you answer this question on GRAPHS and find what D is with working out

can you answer this question on GRAPHS and find what D is with working out

Answer:

[tex](18,14)[/tex]

Step-by-step explanation:

[tex]\mathrm{Since\ AB=BC=CD,\ we\ may\ say\ that\ B\ is\ midpoint\ of\ AC\ and\ C\ is\ midpoint}\\\mathrm{of\ BD.}\\\mathrm{Let\ the\ coordinates\ of\ C\ be\ (x,y)\ and\ D\ be\ (a,b).}\\\mathrm{Using\ midpoint\ formula,}\\\\\mathrm{(6,6)=(\frac{0+x}{2},\frac{2+y}{2})}\\\\\mathrm{or,\ 6=\frac{x}{2}\ and\ y+2=12}\\\\\mathrm{or,\ x=12\ and\ y=10}\\\mathrm{So,\ coordinates\ of\ C\ is\ (12,10).}[/tex]

[tex]\mathrm{As\ C\ is\ midpoint\ of\ BD,}\\\\\mathrm{(x,y)=(\frac{6+a}{2},\frac{6+b}{2})}\\\\\mathrm{or,\ (12,10)=(\frac{6+a}{2},\frac{6+b}{2})}\\\\\mathrm{or,\ 12=\frac{6+a}{2}\ and\ 10=\frac{6+b}{2}}\\\mathrm{or,\ a=18\ and\ b=14}\\\mathrm{So,\ the\ coordinates\ of\ D\ is\ (18,14).}[/tex]

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