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Prove that the area of the triangle whos...

Prove that the area of the triangle whose vertices are `(t ,t-2),(t+2,t+2),` and `(t+3,t)` is independent of `tdot`

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Let `A-=(x_1,y_1)-=(t,t-2), B-=(x_2,y_2)-=(t+2,t+2)`, and `C-=(x_3,y_3)-=(t+3,t)` be the vertices of the given triangle. Then Area of `Delta ABC`
`(1)/(2) |{x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)}|`
`=(1)/(2) |{t(t+2-t)+(t+2)(t-t+2)+(t+2) +(t+3) (t-2-t-2)}|`
`=(1)/(2) |{2t+2t+4-4t-12}|=|-4|=4`sq.units
Clearly, the area of `Delta ABC ` is independent of t.
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