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Inessa [10]
3 years ago
11

A baseball field has four bases that form the shape of a quadrilateral. If someone invented a new game similar to baseball that

had four extra bases in the field, what type of polygon would the bases form?
A. pentagon
B. octagon
C. hexagon
D. decagon
Mathematics
1 answer:
Digiron [165]3 years ago
6 0
The bases would form into a pentagon so A.
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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 ........ <em>(1)</em>

m_{TS} = (- 4 - 1) / (3 - 8 ) = 1 ......... <em>(2)</em>

From (1) and (2) ⇒ NA║TS

m_{AT} = ( 1 - 2) / ( 8 - 1) = - 1 / 7 .......... <em>(3)</em>

m_{NS} = ( - 4 + 3) / ( 3 + 4) = - 1 / 7 .... <em>(4)</em>

From (3) and (4) ⇒ AT║NS

Thus, NATS is rhombus.

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