Collinear Points

Q.

The equation of a line passing through the point of intersection of the lines $x+5y+7=0,3x+2y-5=0$and perpendicular to the line $7x+2y-5=0$, is given by:

1. $2x-7y-20=0$

2. $2x+7y-20=0$

3. $-2x+7y-20=0$

4. $2x+7y+20=0$

Q.

Question 1
The number of lines passing through five points such that no three of them are collinear is
a) 10
b) 5
c) 20
d) 8

Q.

In the figure given below, if OP || RS, ∠OPQ=110^o and ∠QRS=130^o, then ∠PQR is equal to:

1. 

2. 

3. 

4. 

Q.

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

Q. Number of lines which can be drawn from one point:

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

Q.

Consider, three points $P=\left[-\sin \left(\beta -\alpha \right),-\cos \left(\beta \right)\right],Q=\left[\cos \left(\beta -\alpha \right),\sin \left(\beta \right)\right]$ and $R=\left[\cos \left(\beta -\alpha +\theta \right),\sin \left(\beta -\theta \right)\right],\mathrm{where}0<\mathrm{\alpha },\mathrm{\beta },\mathrm{\theta }<\frac{\mathrm{\pi }}{4}$ Then,

1. $P$ lies on the line segment $RQ$

2. $Q$ lies on the line segment $PR$

3. $R$ lies on the line segment $QP$

4. $P,Q$ and $R$ are non – collinear

Q.

Out of $8$ given points, $3$ are collinear. How many different straight lines can be drawn by joining any two points from those $8$ points?

1. $26$

2. $28$

3. $27$

4. $25$

Q.

Find the area of the triangle whose vertices are (0, 4), (0, 0) and (2, 0) by plotting them on the graph.
[4 MARKS]

Q. How many number of lines can we draw through three non-collinear points? (using all the three points)

1. One
2. None
3. Infinite
4. Finite

Q. The minimum number of points required to form a plane is ___

Q. Three or more points which lie on a straight line are called _________ .

1. Concurrent
2. Collinear
3. Parallel
4. Intersecting

Q.

Let $\alpha ,\beta ,\gamma$ be three distinct real numbers. The points with position vectors are $\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k},\beta \hat{i}+\gamma \hat{j}+\alpha \hat{k}\&\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}$

1. Are collinear

2. Form an equilateral triangle

3. Form a scalene triangle

4. Form a right angled triangle

Q.

The 2nd step to draw perpendicular to a given line from an external point is

1. Draw another line parallel to the given line passing through the given point

2. Draw perpendicular bisector of the given line

3. Mark two points on the given line by drawing an arc to the given line from the external point

4. Join midpoint of the line to the external point

Q.

Three or more lines are collinear if they lie on the:

a) same line

b) two lines

c) same plane

d) none of these

Q.

What is the value of point A?

1. 1.60

2. 1.20

3. 1.40

4. 1.50

Q.

Question 2(d):

Which two triangles have $\angle B$ as common?
​​

Q.

If the area of the triangle formed by the points $\left(2a,b\right),\left(a+b,2b+a\right)\mathrm{and}\left(2\mathrm{b},2\mathrm{a}\right)$ is $2sq.\mathrm{units}$, then the area of the triangle whose vertices are $\left(a+b,a-b\right),\left(3b-a,b+3a\right)and\left(3a-b,3b-a\right)$ will be

Q.

Question 6(a):

Consider the following figure of line $\overleftrightarrow{MN}$. Say whether following statement is true or false in the context of the given figure:



Q, M, O, N, P are points on the line $\overleftrightarrow{MN}$

Q. In the adjoining figure, find the total number of right angled triangles.

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

Q. Determine if the points $(1,5),(2,3)$ and $(-2,-11)$ are collinear.

Q.

Given three non-collinear points, only one circle can be drawn through these three points.

1. One

2. Two

Q. What should be the size of piece that would fit in the unknown region?

1. 
2. 
3. 
4. 

Q.

Aju starts from his home and walks x meters in north direction. After that he turns right and walks another x meters. He meets his friends and then reaches back home by the shortest possible path. The area enclosed by the path taken by Aju for the whole journey is 50 m². Find the value of x.

1. 6m

2. m

3. 10m

4. 7m

Q.

The perpendicular drawn on a perpendicular of a line is parallel to the initial line. Is this statement always true ? Justify your answer.

Q. How many lines segments can be drawn to pass through two given points if they are collinear?

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

Q.

In $△$ABC, sides AB = BC =CA. What is this triangle called?

1. Right angled triangle

2. Isosceles triangle

3. 90^o triangle

4. Right angled Isosceles triangle

Q. Find the value of $x$, so that the points $(x,-1),(2,1)$ and $(4,5)$ are collinear.

Q. The points (8, 1) , (3, -4) and (2, -5) are collinear.

1. True
2. False

Q. Choose examples for parallel lines from the given options:

1. 100m Race Track
2. Straight Railway Track
3. Circular Race Track
4. Transmission Lines

Q. Four lines can be drawn through 3 non-collinear points.

1. True
2. False