Sri Chaitanya School 1
Maths - Techno VI - Worksheet - 2
Class : VIII TECHNO
Subject : Mathematics
Topic Name : Collinearity (Analytical Geometry)
WORKSHEET - 5
Objective type questions :
1. If the points (k, 3), (2, 5) and (7, 9) are collinear, then the value of ’k’ is [ ]
a) –1 b)
1
2
c) – 2 d)
1
2
2. If the points A, B, C are collinear, then [ ]
a) area of ABC 0 b) AB2
= AC2
+ BC2
c) slope of AB = slope of BC d) AB + BC = AC
3. If (1, k), (2, 1) and (–2, 5) are coillinear, then k = [ ]
a) 1 b) 2 c) –5 d) –1
4. The points (–1, 7), (3, –5) and (4, –8) are [ ]
a) forms a triangle b) collinear c) non collinear d) both a, c
5. If (1, 2), (–1, b), (–3, –4) are collinear, then b = [ ]
a) 0 b) 1 c) 2 d) –1
6. If (3, –2), (–2, 8) and (x, 4) are collinear, then x = [ ]
a) 0 b) 10 c) 1 d) 15
7. The points (1, 1), (2, 2) and (3, 3) are [ ]
a) forms a triangle b) non collinear c) collinear d) can’t say
Passage type (8 to 10 Questions) :
If three or more points lies on the same line, then the points are called collinear points.
8. If A(–1, 3), B(2, p) and C(5, –1) are collinear, then p = [ ]
a) 0 b) 1 c) 2 d) 3
9. If (y, 2), (2, 3) and (3, 4) are collinear, then y = [ ]
a) –1 b) –2 c) 1 d) 21
10. Vishnu said that the points (1, 2), (2, 2) and (3, 2) are collinear. Priya said that the points are not
collinear. The correct statement given by [ ]
a) Vishnu b) Priya c) Both a, b d) None
Answers
1) ans Area of triangle=
=1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]
= 1/2[k(5-9)+2(9-3)+7(3-5)]
=1/2[5k-9k+12+7(-2)]
=1/2[-4k+12-12]
=1/2[-4k]
2k=0
K= 0
2. ans) area of ABC = 0
3. Ans)
Area of triangle
= 1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]
=1/2[1(1-5)+2(5-k)+(-2)(k-1)]
=1/2[-4+10-2k-2k+2]
=1/2[-4k+4]
-2k+2=0
2k=2, k=1
4. Ans) collinear
5. Ans) area of triangle=
1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]
= 1/2[1(b+4)-1(-4-2)-3(2-b)]
=1/2[b+4+6-6+3b]
=1/2[4b+4]
2b+2= 0
B=-1
6.ans) area of triangle=
1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]
=1/2[3(8-4)-2(4+2)+x(-2-8)]
=1/2[12-12-10x]
=1/2[-10x]
-5x=0
X=0
7. Ans) collinear
8. Ans) area of triangle=
1/2[x1(y2-y3)+x2(y3-y1)+x3(y1-y2)]
= 1/2[-1(p+1)+2(-1-3)+5(3-p)
=1/2[-p-1-8+15-5p]
=1/2[-6p+6]
-3p+3=0
P=1
9. Ans) area of triangle=
=1/2[y(3-4)+2(4-2)+3(2-3)]
=1/2[-y+4-3]
=1/2[-y+1]
10. Ans) vishnu