Write the shape of the quadrilateral formed by joining (1,1) , (6,1) (4,5) and (3,5) * 1 point Trapezium Rectangle Square Circle Other:
Answers
Answer:
A=(−1,−2),B=(1,0),C=(−1,2),D=(−3,0)
By distance formula,
d(A,B)=
(1+1)
2
+(0+2)
2
=2
2
d(B,C)=
(−1−1)
2
+(2−0)
2
=2
2
Also, CD=2
2
,DA=2
2
∴AB=BC=CD=AD ....(1)
Slope of AB=
−2
−2
=1
Slope of BC=
−1−1
2
=−1
Hence, slope of AB × slope of BC =−1
∴AB is perpendicular to BC
The lengths of the adjacent sides are equal and they perpendicular to each other.
Therefore, the polygon is a square.
Step-by-step explanation:
ANSWER
A=(−1,−2),B=(1,0),C=(−1,2),D=(−3,0)
By distance formula,
d(A,B)=
(1+1)
2
+(0+2)
2
=2
2
d(B,C)=
(−1−1)
2
+(2−0)
2
=2
2
Also, CD=2
2
,DA=2
2
∴AB=BC=CD=AD ....(1)
Slope of AB=
−2
−2
=1
Slope of BC=
−1−1
2
=−1
Hence, slope of AB × slope of BC =−1
∴AB is perpendicular to BC
The lengths of the adjacent sides are equal and they perpendicular to each other.
Therefore, the polygon is a square.
