show that the triangle whose vertices are a(-2,4), b(-5,1), c(-6,5) is isosceles
Answers
Answer:
Step-by-step explanation:
We know that the distance between the two points
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
is
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Let the given vertices be
A
=
(
8
,
−
4
)
,
B
=
(
9
,
5
)
and
C
=
(
0
,
4
)
We first find the distance between
A
=
(
8
,
−
4
)
and
B
=
(
9
,
5
)
as follows:
A
B
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
=
√
(
10
−
2
)
2
+
(
1
−
1
)
2
=
√
8
2
+
0
2
=
√
64
=
8
Similarly, the distance between
B
=
(
9
,
5
)
and
C
=
(
0
,
4
)
is:
B
C
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
=
√
(
6
−
10
)
2
+
(
9
−
1
)
2
=
√
(
−
4
)
2
+
8
2
=
√
16
+
64
=
√
80
=
√
4
2
×
5
=
4
√
5
Now, the distance between
C
=
(
0
,
4
)
and
A
=
(
8
,
−
4
)
is:
C
A
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
=
√
(
6
−
2
)
2
+
(
9
−
1
)
2
=
√
4
2
+
8
2
=
√
16
+
64
=
√
80
=
√
4
2
×
5
=
4
√
5
We also know that If any two sides have equal side lengths, then the triangle is isosceles.
Here, since the lengths of the two sides are equal that is
B
C
=
C
A
=
4
√
5
Hence, the given vertices are the vertices of an isosceles triangle.