Collinear Points

Q.

The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.

1. 6

2. 1

3. 4

4. 8

Q.

Find the relation between $x$ and $y$ if the points $(x,y),(1,2)$ and $(7,0)$ are collinear.

Q.

If the points A(1, 2), B(0, 0) and C(a, b) are collinear, then which of the following is correct

1. a = b

2. a = 2b

3. 2a = b

4. a = –b

Q. What is slope of line joining (2, 0) and (0, 3)?

Q.

If the points A(1, 2), B(0, 0), and C(a, b) are collinear, then which of the following is correct?

1. a = b

2. a = 2b

3. 2a = b

4. a = –b

Q. Find the value of ${}^{\prime }{k}^{\prime }$ for which the given point are collinear
$(8,1),(k,-4),(2,-5)$

Q. For 'k' =, the following points (7, -2), (5, 1), (3, k) are collinear.

1. 4
2. 3
3. 5

Q.

Find the values of k, if the points A(k+1, 2k), B(3k, 2k+3) and C(5k-1, 5k) are collinear.

1. k = 2, $\frac{1}{2}$

2. k = 3, $\frac{1}{3}$

3. k = 4, $\frac{1}{4}$

4. k = 5, $\frac{1}{5}$

Q. Values of $k$ for which the quadratic equation $2x^2+kx+k=0$ has equal roots.

1. $4,8$
2. $0,4$
3. $4,-8$
4. $0,8$

Q. In the following, find the value of ‘a’ for which the given points are collinear (2, 3), (4, a) and (6, – 3). (2 marks)

Q.

Find the values of k, if the points A(k+1, 2k), B(3k, 2k+3) and C(5k-1, 5k) are collinear.

1. k = 2, $\frac{1}{2}$

2. k = 3, $\frac{1}{3}$

3. k = 5, $\frac{1}{5}$

4. k = 4, $\frac{1}{4}$

Q.

The value of m, if the points (5, 1) (-2, -3), and (8, 2m) are collinear is:

1. $\frac{15}{14}$

2. $\frac{19}{14}$

3. $\frac{19}{15}$

4. $\frac{19}{17}$

Q. The collection of points which are at a fixed distance from a fixed point is called ______.

1. a line
2. a quadrilateral
3. a circle
4. a triangle

Q. Question 7
Find the value of m, if the points (5, 1) (-2, -3) and (8, 2m) are collinear.

Q.

If the points A(1, 2), B(0, 0), and C(a, b) are collinear, then which of the following is correct?

1. a = b

2. 2a = b

3. a = –b

4. a = 2b

Q.

For what value of k are the points A(k, 2 – 2k) , B(–k + 1, 2k) and C(–4 – k, 6 – 2k) are collinear ? [4 MARKS]

Q.

1. True
2. False

Q.

For what value of 'k' are the following points (7, -2), (5, 1), (3, k) collinear ?

1. 2

2. 5

3. 4

4. 6

Q. Find the relation between 𝒙 and 𝒚 if points (𝟐, 𝟏), (𝒙, 𝒚), and (𝟕, 𝟓) are collinear.

Q.

Find the values of k, if the points A(k+1, 2k), B(3k, 2k+3) and C(5k-1, 5k) are collinear.

1. k = 5, $\frac{1}{5}$

2. k = 2, $\frac{1}{2}$

3. k = 3, $\frac{1}{3}$

4. k = 4, $\frac{1}{4}$

Q. Question 20
If the points A(1, 2), B(0, 0) and C(a, b) are collinear, then
(A) a = b
(B) a = 2b
(C) 2a = b
(D) a = –b

Q. Find the value of m, if the points (5, 1) (-2, -3) and (8, 2m) are collinear.

Q. 83.X = a represents a line parallel to Y axis . Explain?

Q. Question 5
The points A(3, 1), B(12, -2) and C(0, 2) cannot be vertices of a triangle.

Q. For 'k' =, (7, -2), (5, 1), (3, k) are collinear ?

1. 3
2. 4
3. 5

Q. Diameter of a graph denoted by diam (G) is defined by-

1. max{e(v):v$ϵ$ V}
   (where e(v) is eccentricity of vertex, v is a vertex and V is the vertex set)
2. max{d(u, v):u.v$ϵ$V}
   (where d(u, v) is the distance between two vertices U and V)
3. Both 1 and 2
4. None of these

Q. State whether the given statement is true or false. Justify your answer

The points A(3, 1), B(12, -2) and C(0, 2) cannot be vertices of a triangle.

Q. Find the area of $\Delta ABC$ with vertices $A(0,-1),B(2,1)$ and $C(0,3)$. Also, find the area of the triangle formed by joining the midpoints of its sides. Show that the ratio of the areas of these two triangles is $4:1$.

Q.

For what value of k are the points A(k, 2 – 2k) , B(–k + 1, 2k) and C(–4 – k, 6 – 2k) are collinear ? [4 MARKS]

Q. Find the area of $\Delta ABC$ whose vertices are $A(-5,7),B(-4,-5)$ and $C(4,5)$.