Prove that (2, 5), (4, 6) and (8, 8) are collinear point
Answers
Answer:
CBSE Class 10
CBSE
Question Papers874
Textbook Solutions16241
Important Solutions2362
Question Bank Solutions17229
Video Tutorials1380
Time Tables11
LoginCreate free account
Course
CBSE Class 10 CBSE
Question Papers [874]
Textbook Solutions [16241]
Important Solutions [2362]
Question Bank Solutions [17229]
Video Tutorials [1380]
Time Tables [11]
ConceptArea of a Trianglechange
Home
Search
My Profile [view full profile]
why create a profile on Shaalaa.com?
1. Inform you about time table of exam.
2. Inform you about new question papers.
3. New video tutorials information.
Login / Register
QUESTION
Show that the following sets of points are collinear.
(2, 5), (4, 6) and (8, 8)
SOLUTION
The formula for the area ‘A’ encompassed by three points, (x1,y1) (x2,y2)and (x3,y3) is given by the formula,
We know area o triangle formed by three points (x1,y1),(x2,y2),(x3,y3) is given by
Δ
=
1
2
[
x
1
(
y
2
−
y
3
)
+
x
2
(
y
3
−
y
1
)
+
x
3
(
y
1
−
y
2
)
]
Δ=12[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]
If three points are collinear the area encompassed by them is equal to 0
The three given points are A(2, 5), B(4, 6) and C(8, 8). Substituting these values in the earlier mentioned formula we have,
A
=
1
2
[
2
(
6
−
8
)
+
4
(
8
−
5
)
+
8
(
5
−
6
)
]
=12[2(6-8)+4(8-5)+8(5-6)]
=
1
2
[
2
(
−
2
)
+
4
(
3
)
+
8
(
−
1
)
]
=12[2(-2)+4(3)+8(-1)]
=
1
2
[
−
4
+
12
−
8
]
=12[-4+12-8]
=
1
2
[
−
12
+
12
]
=12[-12+12]
=
0
=0
Since the area enclosed by the three points is equal to 0, the three points need to be colliner