Three Points on a Line

Q. If A, B and C are three points on a straight line, and if B lies in between A and C, then which of the following is true?

1. AB + AC = BC
2. BC + AC = AB
3. AB + BC = AC
4. BC - CA = AB

Q. How many planes can be made to pass through two points?

Q.

A point C is called the midpoint of a line segment $\overline{AB}$ if

(a) C is an interior of AB

(b) AC=CB

(c) C is an interior point of AB such that $\overline{AC}=\overline{CB}$

(d) AC+CB=AB

Q.

The number of perpendiculars that can be drawn to a line from a point not on it is

1. $1$

2. $2$

3. $4$

4. Infinitely many

Q. The number of planes passing through 3 noncollinear points is / are ________ .

1. one
2. two
3. three
4. four

Q.

A point C is said to be lie between the points A and B if

(a) AC=CB

(b) AC+CB=AB

(c) points A, C and B are collinear.

(d) none of these

Q.

What is the orthocentre of the triangle formed by the lines $xy=0$, $x+y=0$ is

1. $\left(\frac{1}{2},\frac{1}{2}\right)$

2. $\left(\frac{1}{3},\frac{1}{3}\right)$

3. $\left(0,0\right)$

4. $\left(\frac{1}{4},\frac{1}{4}\right)$

Q. Examine the figure and identify which of the following are collinear points.

1. P, E, C
2. C, F, H
3. C, D, S
4. E, G, H

Q.

For what value of x in the figure, points A, B, C and D are concyclic?

1. 12^o

2. 11^o

3. 9^o

4. 10^o

Q. when to use dot product and when cross product

Q.

How many perpendiculars can be drawn from a point on the line$?$

Q. If A, B and C are collinear points, then name all the line segments.

1. AB, AC
2. AB
3. BC, BA
4. AB, BC and AC

Q.

Draw any line segment, say . Take any point $\mathrm{C}$ lying in between $\mathrm{A}$ and $\mathrm{B}$. Measure the lengths of $\mathrm{AB},\mathrm{BC}$ and $\mathrm{AC}$. Is $\mathrm{AB}=\mathrm{AC}+\mathrm{CB}$? [Note: If $\mathrm{A},\mathrm{B},\mathrm{C}$ are any three points on a line, such that $\mathrm{AC}+\mathrm{CB}=\mathrm{AB},$ then we can be sure that $\mathrm{C}$ lies between $\mathrm{A}$ and $\mathrm{B}$.

Q. If A, B and C are three points on the line (in the same order), then which of the following is true?

1. AB+BC = AC.
2. AB=BC=AC
3. AB+BC > AC.
4. AB+BC < AC.

Q. in triangle pqr angle qpr =angle pqr and m, n are points on sides qr and pr respectively such that qm= pn prove that op = o

Q. If AB = CD and CD = 2 EF then

1. AB = EF
2. AB = 2 EF
3. AB = 3 EF
4. AB = 4 EF

Q. How many nodal plane present in *2px??

Q.

A, B and C are three collinear points such that A lies between B and C.

Name all the line segments determined by these points and write the relation between them.

Q. If A, B and C are three points on the line (in the same order), then which of the following is true?

1. AB+BC > AC.
2. AB+BC < AC.
3. AB+BC = AC.
4. AB=BC=AC

Q. If AB = CD and CD = EF then

1. AB = EF
2. AC = BD
3. DE = CF
4. DF = CE

Q.

A point $\mathrm{C}$ is called the midpoint of a line segment $\mathrm{AB}$, if

1. $\mathrm{C}$ is an interior point of $\mathrm{AB}$

2. $\mathrm{AC}=\mathrm{CB}$

3. $\mathrm{C}$ is an interior point of $\mathrm{AB}$ such that $\mathrm{AC}=\mathrm{CB}$

4. $\mathrm{AC}+\mathrm{CB}=\mathrm{AB}$

Q.

When $a=-1,b=0$ then find the value of $2a+3b$

Q. In the given figure, if AC = BD, show that AB = CD. State Euclid's axiom used for it.
Figure

Q. Distance of the point A(x, y) from the origin O is __

1. OA² = x² - y²
2. OA² = x² + y²
3. OA = x² + y²
4. OA² = x + y

Q. Assertion: Every line segment has a unique mid-point.
Reason: A point C is called the mid-point of a line segment AB if C is an interior point of AB and AC = CB.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Q. If R is point between C and D and CR = RD; then

1. CD = 2 RD
2. CD = 0.5 RD
3. CD = 0.25 RD
4. CD = 0.75 RD

Q. Greeks emphasised
(a) inductive reasoning
(b) deductive reasoning
(c) practical use of geometry
(d) analytical geometry

Q. A, B, C are three points on a straight line. If AB = BC and AC = 4 units then

1. AB = 2
2. BC = 8
3. AB =4
4. BC = 4

Q. A, B, C are three points on a straight line. If AB = BC and AC = 4 units then

1. AB = 2 units
2. BC = 4 units
3. BC = 8 units
4. AB = 4 units

Q. A point C is said to lie between the points A and B if
(a) AC = CB
(b) AC + CB = AB
(c) points A, C and B are collinear
(d) None of these