★show that the points:
A (a, a) ,B(-a, a), C (-a√3, a√3)
we need to show that these points that an equilateral triangle.
Answers
Answered by
0
Answer:
sry friend no idea about the answer
Answered by
1
Step-by-step explanation:
Let the points be represented by A(a,a),B(−a,−a) and C(−a
3
,a
3
). Using the distance formula
d=
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
, we have
AB=
(a+a)
2
+(a+a)
2
=
(2a)
2
+(2a)
2
=
4a
2
+4a
2
=
8a
2
=2
2
a
BC=
(−a
3
+a)
2
+(a
3
+a)
2
=
3a
2
+a
2
−2a
2
3
+3a
2
+a
2
+2a
2
3
=
8a
2
=
4×2a
2
=2
2
a
CA=
(a+a
3
)
2
+(a−a
3
)
2
=
a
2
+2a
2
3
+3a
2
+a
2
−2a
2
3
+3a
2
=
8a
2
=2
2
a
∴AB=BC=CA=2
2
a.
Since all the sides are equal the points form an equilateral triangle.
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