Finding Area of a Triangle using Determinants (includes example) Video Lecture | Mathematics (Maths) Class 12 - JEE

hello friends this video on determinants
part 19 is brought you by exam viacom no
more fear from exam before watching this
video please make sure that you have
watched part 1 to part 18 now we will
study application of determine to find
area of triangle so if you have a
triangle with vertices x1 y1 x2 y2 x3 y3
so 3 vertices are threes in that case we
can find the area of triangle to be 1 by
2 x1 y2 minus y3 plus y2 x2 into y 3
minus y1 plus x3 into bio minus YT the
same thing can be represented in the
form of determinant area of triangle is
nothing but 1 by 2 into x1 y1 x2 y2 x3
y3 and you put 1 1 1 here because this
is defined only for square matrix so we
have to make it 3 draws 3 and that's why
we put 1 1 1 here and thus we get area
of triangle to be 1 by 2 X 1 y 1 1 X 2 y
2 1 X 3 y 3 1 please note this formula
it's a critical for me I will be using
this area of triangle to be 1 by 2
determinant of x 1 y 1 1 x 2 y 2 1 x 3 y
3 1 and please note the area of triangle
is always positive because the area is
always positive so we always take
absolute value for determinants so this
is nothing but absolute value of this
even if comes out to be negative we take
the positive part absolute well we'll
take some example for area of triangle
let's try to find the area of the
triangle with the vertices 1 0 6 0 4 3
so here if you see we have this triangle
with vertices 1 0 6 0 and 14 and the
area of triangle formula is very simple
1 by 2 into X 1 Y 1 1
x2 y2 1 x3 y3 1 now what is x1 y1 the
first virtus 1 0 x2 y2 second what is 6
0 and x3 y3 is 4 so this is my area of
prime that we just saw this so if you
saw this this comes out to be 1 into 0
minus 3 minus 0 plus 1 into 6 into 3 18
minus 0 this is nothing but 1 by 2 into
0 minus 3 is minus 3 minus 3 plus 18 is
15 1 by 2 into 15 that is 15 by 2
squaring it very simple we have the
points x1 y1 x2 y2 x3 y3 this put the
points in the formula find it the minute
get the answer and take one more example
because we'll have to a very critical
topic to find the area so let's find
area another triangle with the vertices
minus 2 minus 3 3 2 minus 1 and a same
thing here so this guy is x1 y1 x2 y2
this guy is x3 y3 so area formula is
nothing but 1 by 2 determinant of X 1 Y
1 1 x2 y2 1 x3 y3 1 correct this guy is
nothing but 1 by 2 determinant of X 1 is
minus 2 y 1 is minus 3 and 1 X 2 is 3 y
2 is 2 and 1 X 3 is minus 1 y 3 is minus
8
and one just lets all this 1 by 2 minus
2 into 2 min to 1 minus minus 18 to
borrow correct minus minus 3 into 3 into
1 minus 1 into 1 3 into 1 minus 1 into
minus 1 correct
and then plus 1 into 8 into minus 3 or
minus 8 into 3 minus 2 minus 1 this
comes out to be 1 by 2 written mod of
minus 2 into this is 2 minus minus a 2
plus 8 10 minus 2 into 10 is minus 20
minus 3 minus minus 3 plus 3 plus 3 into
3 plus 1 for 4 in degrees 12 plus 12
this guy becomes minus a 2 3 is minus 24
plus 2 minus 20 minus windy this guy is
nothing but 1 by 2 into minus 30 correct
and this guy's nothing but 15 minus 15
but we take absolute volume value of a
so I take the absolute value of this
this becomes 15 unit or square and if
you have teal square and that is my
answer so this question I took because
the answer came out to be minus 15 and
we have to note here that the area of
triangle is always positive so I will
take the absolute value absolute value
of minus 15 is 15 thank you
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