Answer:
Step-by-step explanation:
NA = √[(- 4 - 1 )² + (- 3 - 2)²] = 5√2
AT = √[(8 - 1 )² + (1 - 2)²] = 5√2
TS = √[(3 - 8 )² + (- 4 - 1)²] = 5√2
NS = √[(- 4 - 3 )² + (- 3 + 4)²] = 5√2
NA = AT = TS = NS = 5√2
[tex]m_{NA}[/tex] = (- 3 - 2) / (- 4 - 1) = 1 ........ (1)
[tex]m_{TS}[/tex] = (- 4 - 1) / (3 - 8 ) = 1 ......... (2)
From (1) and (2) ⇒ NA║TS
[tex]m_{AT}[/tex] = ( 1 - 2) / ( 8 - 1) = - 1 / 7 .......... (3)
[tex]m_{NS}[/tex] = ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... (4)
From (3) and (4) ⇒ AT║NS
Thus, NATS is rhombus.
