Constructing a Line Segment of a Given Length

Q.

Draw any $△PQR$. Through $P$, draw a line parallel to $QR$.

Q.

A line segment PQ is written as $\overleftrightarrow{PQ}$.

1. True
2. False

Q.

In the given figure, Find the value of q.

1. ${90}^{\circ }$

2. ${48}^{\circ }$

3. ${42}^{\circ }$

4. ${110}^{\circ }$

Q. Bisect a straight angle, using ruler and compasses. Measure each part.

Q.

To divide a line segment $AB$in the ratio $5:7$, first a ray $AX$ is drawn so that $BAX$is an acute angle and then at equal distances points are marked on the ray $AX$ such that the minimum number of these points is

1. $8$

2. $10$

3. $11$

4. $12$

Q. Draw any line segments $\overline{AB}$. Mark any point $M$ on it. Through $M$, draw a perpendicular to $\overline{AB}$.
(use ruler and compasses)

Q. Draw a line segment of length 9 cm using ruler and compass. Divide this line segment into three equal parts.

Q. Construct a $\Delta ABC$ in which $CA=6cm,AB=5cm$ and $\angle BAC={45}^o$. Then construct a triangle whose sides are $\frac{3}{5}$ of the corresponding sides of $\Delta ABC$.

Q. Draw a line segment $AB$ using a ruler and compass, obtain a line segment of length $\frac{3}{4}\left(AB\right)$.

Q. You have a compass with a pencil. Which of the following you must have to draw a line segment of 10 cm?

1. A protractor.
2. A ruler of 15 cm.
3. A set square.
4. A divider.

Q. Draw a line segment $MN=10cm$. Using ruler and compass, divide it into $4$ equal parts.

Q.

Line segment $\overline{AB}$ is alinged along the ruler as shown below $.$ Write its length $.$

Q.

Draw a line segment of the length $6.6cm$. Bisect it and measure the length of each part.

Q. Draw a line $AB=7.8cm$, what will be the $\frac{2}{3}$rd of $AB$.

1. $11.7cm$
2. $5.2cm$
3. $3.9cm$
4. $2.6cm$

Q. Draw a line $XY=13.6cm$. what will be the $\frac{1}{4}$th of $XY$ ?

1. $6.8cm$
2. $5.2cm$
3. $2.2cm$
4. $3.4cm$

Q.

Question 1

Draw any line segment $\overline{PQ}$. Without measuring $\overline{PQ}$, construct a copy of $\overline{PQ}$

Q. The time and distance travelled by a cyclist is given below in the graph. The equation representing the straight line is

1. y = 2x + 3
2. y = x + 4
3. y = 3x + 2

Q. Draw a line segment of length $7.2cm$ and divide it in the ratio $5:3$. Measure the two parts.

Q. You have a compass with a pencil. Which of the following you must have to draw a line segment of 10 cm.

1. A ruler of 15 cm
2. A protractor
3. A set square
4. A divider

Q. Construct $\overline{AB}$ of length 7.8 cm. From this, cut off $\overline{AC}$ of length 4.7 cm. The measure of $\overline{BC}$ is .

1. 4.7 cm
2. 3.1 cm
3. 7.4 cm
4. 1.3 cm

Q. Construct a line segment of length $4.6\text{cm}$. Divide this line into $2$ equal parts and find the length of each part.

1. $2.0\text{cm}$
2. $2.1\text{cm}$
3. $2.2\text{cm}$
4. $2.3\text{cm}$

Q. Draw a line segment of length $4.9$ cm and divide it in the ratio $3:4$ , measure the two parts.

Q. Construct $\overline{AB}$ of length $7.8cm$. Find this, cut off $AC$ of length $4.7cm$ . Measure $\overline{BC}$

Q. Construct a line segment of length $12.4cm$. Divide this line into $4$ equal parts and find the length of each part.

1. $3.1cm$
2. $3.0cm$
3. $4.1cm$
4. $4.0cm$

Q. Draw the graph of $x+2y=4$

Q. The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.
Which of the above steps comes first?

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

Q. Construct a line $AB=6.5cm$. What will be the $\frac{1}{5}$th of $AB$ ?

1. $3.5cm$
2. $4.2cm$
3. $2.4cm$
4. $1.3cm$

Q.

Question 4

Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement

Q. Draw a line, say, $MN$. From a point $P$ outside it, draw a line parallel to $MN$ using ruler and and compasses only.

Q. Which of the following line segments can be drawn with the help of a ruler and compass ?

1. $1.234cm$
2. $2.15cm$
3. $2.5cm$
4. $3.04cm$