in the figure ABCD is the. AB =6 cm, BC=3 cm. S, T, യൂ, V and W are the points on the line DC which is extended to both sides. ADB, ATB, AUB, ACB, AVB and AWB are the triangles whose base is AB and third vertices lie on the line DC which is extended to both sides. (a) what are the special features of the sides AB and SW? (b) what is the area of the triangle ABC? (c) Compute the areas of the triangles ASB, ATB, AUB, AVB, AWB?
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We have given points are
A(x
1
,y
1
)=(3,5)
B(x
2
,y
2
)=(6,0)
C(x
3
,y
3
)=(1,−3)
D(x
4
,y
4
)=(−2,2)
Then,
Distance between
AB=
(x
1
−x
2
)
2
+(y
1
−y
2
)
2
=
(3−6)
2
+(5−0)
2
=
9+25
AB=
34
BC=
(x
2
−x
3
)
2
+(y
2
−y
3
)
2
=
(6−1)
2
+(0+3)
2
=
25+9
BC=
34
CD=
(x
3
−x
4
)
2
+(y
3
−y
4
)
2
=
(1+2)
2
+(−3−2)
2
=
9+25
CD=
34
DA=
(x
4
−x
1
)
2
+(y
4
−y
1
)
2
=
(−2−3)
2
+(2−5)
2
=
25+9
DA=
34
Then, AB=BC=CD=DA
All sides are equal.
Hence, ABCD is a square.
Step-by-step explanation:
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