Collinearity Condition

Q.

How do you find the value of $\cos (300°)$?

Q.

Find the value of 'k', for which the points (8, 1), (k, -4), (2, -5) are collinear.

1. 2

2. 3

3. 1

4. 4

Q.

How many terms of the series 54, 51, 48, .... be taken so that their sum is 513 ? Explain the answer.

Q. If Points (1, 2) (−5, 6) and (a, −2) are collinear, then a =

(a) −3

(b) 7

(c) 2

(d) −2

Q.

If $a>b>0$, then the value of ${\tan }^{-1}\left(\frac{a}{b}\right)+{\tan }^{-1}\left(\frac{a+b}{a-b}\right)$

1. both $a$ and $b$

2. $b$ but not $a$

3. $a$ but not $b$

4. neither $a$ nor $b$

Q.

The area of triangle OAB with O (0, 0), A (4, 0) & B (0, 6) is ________________

Q. The value of k for which the points (7, -2), (5, 1), (3, k) collinear is _____.

1. 4

Q. Points A(−1, y) and B(5, 7) lie on a circle with centre O(2, −3y). Find the values of y. [CBSE 2014]

Q. If the centroid of a triangle is (1, 4) and two of its vertices are (4, −3) and (−9, 7), then the area of the triangle is

(a) 183 sq. units

(b) $\frac{183}{2}$ sq. units

(c) 366 sq. units

(d) $\frac{183}{4}$ sq. units

Q.

The value of m for which the points (3, 5), (m, 6) and $(\frac{1}{2},\frac{15}{2})$ are collinear is

1. 1
2. 2
3. 3
4. 4

Q.

If the points A(x, 2), B(-3, -4) and C(7, -5) are collinear then the value of x is

(a) -63 (b) 63 (c) 60 (d)-60

Q. Prove that the points (−2, 5), (0, 1) and (2, −3) are collinear.

Q.

If three points $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ lie on the same line, prove that $\frac{y_2-y_3}{x_2{x}_3}+\frac{y_3-y_1}{x_3{x}_1}+\frac{y_1-y_2}{x_1{x}_2}=0.$

Q.

Prove that the points A(a, 0), B(0, b) and C(1, 1) are collinear, if $\frac{1}{a}+\frac{1}{b}=1$.

Q.

If $A>0,B>0$ and $A+B=\frac{\pi }{3}$, then the maximum value of $\tan \left(A\right)\tan \left(B\right)$ is

1. $\frac{1}{2}$

2. $\frac{1}{3}$

3. $\frac{1}{4}$

4. $\frac{1}{6}$

Q. Find the value of k, if the point P (2, 4) is equidistant from the points A (5, k) and B (k, 7).

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. 2
2. $\frac{1}{2}$
   
3. 4
4. $\frac{1}{4}$

Q.

If $a_1,a_2,.....a_n$ is an AP with a common difference $d$, then $\tan \left[{\tan }^{-1}\left(\frac{d}{1+a_1{a}_2}\right)+{\tan }^{-1}\left(\frac{d}{1+a_2{a}_3}\right)+........+{\tan }^{-1}\left(\frac{d}{1+a_{n-1}{a}_n}\right)\right]$

1. $\frac{(n-1)d}{a_1+a_n}$

2. $\frac{(n-1)d}{1+a_1{a}_n}$

3. $\frac{nd}{1+a_1{a}_n}$

4. $\frac{(a_n-a_1)}{(a_n+a_1)}$

Q. If the point P(k − 1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k. [CBSE 2014]

Q. 14 Three points (0, 0) , (3, root 3), (3, lamda ) form an equilateral triangle , then lamda is eqial to ?

Q.

If R (x, y) is a point on the line segment joining the points P (a, b) and Q (b, a) then prove that x + y = a +b.

Q.

Find the value (s) of k for which the points $(3k-1,k-2)$, $(k,k-7)$ and $(k-1,-k-2)$ are collinear.

Q. If points (t, 2t), (−2, 6) and (3, 1) are collinear, then t =

(a) $\frac{3}{4}$

(b) $\frac{4}{3}$

(c) $\frac{5}{3}$

(d) $\frac{3}{5}$

Q.

If the points A(7, -2), B(5, 1) and C(3, k) are collinear, then the value of K is:

1. 8

2. 6

3. 4

4. 2

Q. Find the value of k so that the area of the triangle with vertices A(k + 1, 1), B(4, −3) and C(7, −k) is 6 square units.

Q.

Prove that the points (a, b) , $(a_1,b_1)$ and $(a-a_1,b-b_1)$ are collinear if $a{b}_1=a_{1}b$.

Q. If A(−3, 5), B(−2, −7), C(1, −8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area. [CBSE 2014]

Q.

Find the value of K for which the points (2, 5), (K, 11/2), (4, 6) are collinear

1. 1/3

2. -1/3

3. 3

4. -3

Q.

Find area of the triangle whose vertices are $\left(-5,-1\right)$, $\left(3,-5\right)$ and $\left(5,2\right)$

Q.

Show that the following points are collinear :

(i) A (2, -2), B(-3, 8) and C(-1, 4)

(ii) A(-5, 1), B(5, 5) and C(10, 7)

(iii) A(5, 1), B(1, -1) and C(11, 4)

(iv) A(8, 1), B(3, -4) and C(2, -5)