Question

prove that the area of a triangle which vertices (t,t-2),(t+2,t+2),and (t+3,t) is independent of t.

Answer 1

given three points are (t, t-2) , (t+2, t+2) and (t+3, t)

use formula of traingle form of co-ordinate geometry .

area of traingle =1/2 {x1 (y2-y3)+x2 (y3-y1)+x3(y1-y2)}

now,
ar of triangle=1/2 {t (t+2-t)+(t+2)(t-t+2)+(t+3 (t-2-t-2)}
=1/2 {2t +2t +4 -4t -12}
=1/2 {-8}
=-4
but here mention only magnitude of area of triangle so , area of traingle =4 sq unit
you see in area of triangle not depend upon t

Answer 2

Step-by-step explanation:

i think this will helpfull