Division of a Line Segment

Q. In a parallelogram ABCD, what should be the location of a point E on AB such that if a line parallel to BC = 3 cm is drawn from E, a rhombus is formed? (AB > BC)

1. 6 cm from point A
2. 1.5 cm from point A
3. 3 cm from point A
4. Data Insufficient

Q. How can we construct a rhombus inside a parallelogram in which the smaller side is two-third the larger side?

1. Using the length of the longer side construct a rhombus by extending the smaller side.
2. Find the point which divides the larger side in the ratio of 2:1 and then draw a line parallel to smaller side.
3. Measure with a scale and identify the point on the larger side and construct a rhombus.
4. Find the point which divides the larger side in the ratio of 2:3 and then draw a line parallel to smaller side.

Q. While dividing a segment in a given ratio, we can not draw the ray at angles ______ and _____.

1. $0^{\circ }$
2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. ${136}^{\circ }$

Q. The number of arcs that have to be drawn on ray BX which is at an acute angle to BC so as to divide BC in the ratio of 2:3.

1. 3
2. 5
3. 2
4. 6

Q. How do we identify two points P and Q on a line segment AB such that AP : PQ = 1 : 2 and PQ : QB = 4 : 5?

1. The point P is mid point of AB and Q is mid point of line segment PB. Identify the points P and Q by dividing AB accordingly.
2. Find the ratios in which the points P and Q divide line segment AB and then divide the line segment AB in the ratios obtained.
3. The points P and Q are points of trisection of the line segment AB. Identify the points P and Q by dividing AB into three equal parts.
4. None of the above

Q.

Mention the proper order of identifying a point D on BC such that $\frac{BD}{DC}=\frac{2}{3}$.
1) Join $B_{5}C$ and draw a line parallel to $B_{5}C$ from $B_2$.
2) Identify the ratio in which the point D divides BC using the relation given.
3) Mark 5 points B₁, B₂, B₃, B₄ and B₅ on BX such that they are equidistant.
4) Construct a ray BX which makes an acute angle with line segment BC.
5) The point of intersection of the parallel line from B₂ with BC is the point D.

1. 2, 4, 3, 1, 5

2. 1, 2, 4, 3, 5

3. 4, 3, 2, 5, 1

4. 3, 5, 2, 4, 1

Q.

To divide AB in the ratio 5:1, after some stages, we draw an arc with centre at $A_6$, repeat the same with equal radius at $A_5$. Then mark the first arc ($A_6$ and $A_5$) at $C_1$ and mark the same for second arc ($A_5$ and $A_4$) at $C_2$. This is done in order to:

1. Make the diagram attractive .

2. Draw a line $A_6{B}^{\prime }$ through $C_2$.

3. Draw an angle at $A_5$ equal to $\angle$ $A{A}_{6}B$.

4. Draw $A^{\prime }{C}_2\parallel A{A}_6$

Q.

To divide a line segment PQ in a certain ratio, we draw a ray PM. Why don’t we draw it with an obtuse angle?

1. We cannot measure an obtuse angle with the given line segment.

2. The textbook says we should draw an acute angle.

3. Drawing an obtuse angle would make my constructions very congested.

4. The diagram would be very large.

Q.

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects the line XY at point P at the same angle of inclination as AB. Line PQ is _________ to line segment AB.

1. perpendicular

2. bisector

3. concurrent

4. parallel

Q.

State whether true or false:
To divide a line segment, the constructed ray must be at an obtuse angle to the line segment.

1. True

2. False