Math, asked by neelaveni5047, 10 months ago

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

Answered by Sukhpreet85
1

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

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