Question

I neeed help plz 30 points

Answer 1

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

$m_{NA}$ = (- 3 - 2) / (- 4 - 1) = 1 ........ (1)

$m_{TS}$ = (- 4 - 1) / (3 - 8 ) = 1 ......... (2)

From (1) and (2) ⇒ NA║TS

$m_{AT}$ = ( 1 - 2) / ( 8 - 1) = - 1 / 7 .......... (3)

$m_{NS}$ = ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... (4)

From (3) and (4) ⇒ AT║NS

Thus, NATS is rhombus.