Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
An equilateral triangle has each side equal to
a
a
a
. If the coordinates of its vertices are
(
x
1
,
y
1
)
(x_1, y_1)
(
x
1
,
y
1
)
,
(
x
2
,
y
2
)
(x_2, y_2)
(
x
2
,
y
2
)
and
(
x
3
,
y
3
)
(x_3, y_3)
(
x
3
,
y
3
)
then the square of the determinant
∣
x
1
y
1
1
x
2
y
2
1
x
3
y
3
1
∣
\begin{vmatrix} x_1 & y_1 & 1 \\ x_2 & y_2 & 1 \\ x_3 & y_3 & 1 \end{vmatrix}
x
1
x
2
x
3
y
1
y
2
y
3
1
1
1
equals a.
3
a
4
3a^4
3
a
4
b.
3
a
4
2
\frac{3a^4}{2}
2
3
a
4
c.
3
4
a
4
\frac{3}{4}a^4
4
3
a
4
d.
3
8
a
4
\frac{3}{8}a^4
8
3
a
4
Browse the problem library