Question

Prove that the area of the triangle whose vertices are (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 triangle form of coordinate geometry.

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

now, using formula ,
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

Answer:

Step-by-step explanation:

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

use formula of triangle form of coordinate geometry.

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

now, using formula ,

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