Is there an easy way to find the sign of this determinant without calculating it directly?

Multi tool use
up vote
0
down vote
favorite
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
favorite
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
yesterday
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
There exist real numbers $A_x, A_y, B_x, B_y, C_x, C_y, D_x$ and $D_y$. Is there an easy way to find the sign of following determinant without calculating it directly? BTW, the determinant appears when judging whether or not point $D$ is inside the circumcircle of triangle $ABC$ on the plane.
$$
left|
begin{array}{ccc}
A_x - D_x & A_y - D_y & (A_x - D_x)^2 + (A_y - D_y)^2 \
B_x - D_x & B_y - D_y & (B_x - D_x)^2 + (B_y - D_y)^2 \
C_x - D_x & C_y - D_y & (C_x - D_x)^2 + (C_y - D_y)^2
end{array}
right|
$$
determinant triangle circle triangulation
determinant triangle circle triangulation
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited yesterday
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 15 at 18:29
cia_rana
1012
1012
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
cia_rana is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
yesterday
add a comment |
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
yesterday
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
yesterday
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
yesterday
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
cia_rana is a new contributor. Be nice, and check out our Code of Conduct.
cia_rana is a new contributor. Be nice, and check out our Code of Conduct.
cia_rana is a new contributor. Be nice, and check out our Code of Conduct.
cia_rana is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3000082%2fis-there-an-easy-way-to-find-the-sign-of-this-determinant-without-calculating-it%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Myc,c,AjfT
At a glance, this would be way easier to read if the subscripts were removed and every argument was just assigned a single letter.
– The Count
yesterday