Answer:
Question:
A triangle has a perimeter of exactly 24 units. Which of the following could be the vertices of the triangle?
A.) (-1,3),(2,-1),(-1,-1)
B.) (6,0),(6,7)(0,7)
C.) (-1,-1),(-6,-13),(-9,-9)
D.) (-3,-4),(3,-4),(3,4)
Triangle and Coordinate Geometry
As the name suggests 'tri-angle' means it has three angles that are formed only when three sides are joined together.
So the triangle is a planner geometry that has three sides and three interior angles. In a triangle, the sum of all three interior angles is always
180
∘
.
If a triangle
A
B
C
has the sides
a
,
b
,
and
c
, then
The perimeter of the triangle:
P
=
a
+
b
+
c
In coordinate geometry, the distance between two points:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Answer and Explanation:
Given:
The perimeter of the triangle is
24
units.
There are four options with different-different vertices and one of them is correct, so we choose one option randomly and check it for the given perimeter.
Firstly we chose the option
D
:
The vertices of the triangle are:
P
(
−
3
,
−
4
)
,
Q
(
3
,
−
4
)
,
and
R
(
3
,
4
)
Using the distance formula:
D
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
So
P
Q
=
√
(
3
+
3
)
2
+
(
−
4
+
4
)
2
=
√
6
2
+
0
=
6
u
n
i
t
And
Q
R
=
√
(
3
−
3
)
2
+
(
4
+
4
)
2
=
√
0
+
8
2
=
8
u
n
i
t
And
P
R
=
√
(
3
+
3
)
2
+
(
4
+
4
)
2
=
√
6
2
+
8
2
=
√
36
+
64
=
√
100
=
10
u
n
i
t
So
The perimeter of the triangle
P
Q
R
is:
Perimeter
=
P
Q
+
Q
R
+
P
R
=
6
+
8
+
10
=
24
u
n
i
t
s
Step-by-step explanation: