the vertices of a triangle (2,3) , (3,5) and (-1,4) . show that the triangle is scalene .
Answers
Answer:
Step-by-step explanation:
f we label them A(13,-2) B(9-8) and C(5-2)
The distance between A and B:
13
⇒
9
=
4
−
2
⇒
−
8
=
6
4
2
+
6
2
=
52
so the distance is
√
52
The distance between B and C:
9
⇒
5
=
4
−
8
⇒
−
2
=
6
4
2
+
6
2
=
52
the distance is
√
52
The distance between A and C is 8 as they are both on -2 for
y
The distances AB and BC are
√
52
and therefore isosceles.
Answer link
sjc
May 7, 2018
see below
Explanation:
An isosceles triangle is one with two equal lengths.
To find the lengths of the sides with coordinates
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
we use Pythagoras' theorem
d
=
√
(
x
2
−
x
2
)
2
+
(
y
2
−
y
1
)
2
from the information given
d
1
=
√
(
13
−
9
)
2
+
(
−
2
−
−
8
)
2
d
1
=
√
4
2
+
6
2
=
√
52
−
−
(
1
)
d
2
=
√
(
13
−
5
)
2
+
(
−
2
−
−
2
)
2
d
2
=
√
8
2
+
0
2
=
√
64
=
8
−
−
(
2
)
d
3
=
√
(
9
−
5
)
2
+
(
−
8
−
−
2
)
2
d
3
=
√
4
2
+
6
2
=
√
52
−
−
−
(
3
)
we see
d
1
=
d
3
since we have two equal sides the triangle with the given vertices is isosceles