I neeed help plz 30 points Quadrilateral NATS has coordinates N(-4, -3), A(1, 2), T(8, 1), and S(3, -4). Prove that quadrilateral NATS is a rhombus. Give your statement with the equal distances. Remember to identify the sides.

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

= (- 3 - 2) / (- 4 - 1) = 1 ........ (1)

= (- 4 - 1) / (3 - 8 ) = 1 ......... (2)

From (1) and (2) ⇒ NA║TS

= ( 1 - 2) / ( 8 - 1) = - 1 / 7 .......... (3)

= ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... (4)

From (3) and (4) ⇒ AT║NS

Thus, NATS is rhombus.

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step-by-step explanation: