Question

Consider three points on the
x
y
−
coordinate plane
A
=
(
3
,
−
7
)
,
B
=
(
6
,
−
14
)
and
C
=
(
−
9
,
21
)
. Which of the following statements is/are true?

If we consider these three points to be the vertices of a triangle, then the area is
0
.

If we consider these three points to be the vertices of a triangle, then the area is
168
square units.

The points
A
,
B
and
C
are collinear.
In general, if the area of a triangle considering any three points be zero then the three points are collinear.​

Answer 1

Answer:

the point a b c is collinear

Answer 2

Solution :-

we know that, Area of ∆ with three vertices ,

• A = (1/2)[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)] .

putting given values we get,

→ A = (1/2)[3(-14-21) + 6(21+7) - 9(-7 + 14)]

→ A = (1/2)[3 * (-35) + 6 * 28 - 9 * 7]

→ A = (1/2)[-105 + 168 - 63]

→ A = (1/2)[168 - 168]

→ A = 0 .

since Area of ∆ is equal to zero.

therefore, we can conclude that, the three given points are collinear .

Hence, statement (1), (3) and (4) are true .

Learn more :-

find the centroid of the triangle whose vertices are (2, -3), (-4, 2)and(8, 13).

https://brainly.in/question/38194181

The orthocentre of the triangle with vertices A (1 , 3), B(2 , -1) and C ( 0 , -3)

https://brainly.in/question/35183021