Constructing Perpendicular to a Line through a Point on the Line

Q.

Draw a line $l$ and a point $X$ on it. Through $X$, draw a line segment perpendicular to $l$.Now draw a perpendicular to $\overline{XY}$ at $Y$. (use ruler and compasses)

Q.

The following diagram shows parallel lines cut by a transversal. Find x.

1. 

2. 

3. 

4. 

Q.

Draw a circle. Now draw any of its two diameters and mark them AC and BD. Join the points A, B, C and D. If ABCD is a square, the diameters must be ___ to each other.

Q.

Draw the perpendicular bisector of $XY$ whose length is $10.3$cm.

(a) Take any point P on the bisector drawn. Examine whether $PX=PY$.

(b) If M is the midpoint of $XY$, what can you say about the lengths $MX\&XY$ ?

Q.

Draw a circle of radius $4cm.$ Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

Q. draw a line segment of length 12.8 CM using compass divide it into 4 equal parts verified by actual measurement

Q.

Draw any line segment $PQ$. Take any point $R$ not on it. Through $R$, draw a perpendicular to $PQ$(use ruler and set-square).

Q. We can verify the construction of a perpendicular to a line segment using a

1. ruler
2. compass
3. protractor
4. pencil

Q.

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

Q. How many arcs will we need to make while constructing a perpendicular to a line at a point on the line using a compass.

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

Q.

Draw a line segment AB of length 8 cm. At each end of this line segment, draw a line perpendicular to AB. Are these two lines parallel?

Q.

Define line segment and construct a line segment AB of length 3.9 cm using compasses and ruler. [2 MARKS]

Q.

Using a set square and a ruler construct a line perpendicular to given line at a point on it.

Q. Construct a line segment perpendicular to line segment $AB=12$ $cm.$

Q. The steps to construct a line perpendicular to $XY$ and passing through $P$ is given in random order :
$1.$ Move the set square along XY so the other short side touches Point P.
$2.$ Use the edge of the set square to draw a line through Point P.
$3.$ Draw a line $XY$ and mark point $P$.
$4.$ Place one short side of the set square on the line XY.
Which of the following will be the second step :

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

Q. The angle that is common to the two different types of set squares is

1. ${90}^{\circ }$
2. ${60}^{\circ }$
3. ${30}^{\circ }$

Q. Using a set square and a ruler draw a line parallel to the given line through a point $5$ $\text{c}m$ above it.

Q. A perpendicular bisector of a given line to it.

1. is perpendicular
2. is parallel
3. is circular
4. is a point

Q. The following table represents the relation between x and y. Which of the following graph shows the missing values in the given table?

1. 
2. 
3. 
4. 

Q.

You can draw a perpendicular using a ruler and a _________ as also a ruler and a _______.

Q. Given AB of length 8.5 cm and CD of length 5.6 cm, construct a line segment XY such that the length of XY is equal to the difference between the lengths of AB and CD. Verify by measurement.

Q. Draw a line $l.$ Draw a perpendicular to $l$ at any point on $l.$ On this perpendicular choose a point $X,4cm$ away from $l$. Through $X,$ draw a line $m$ parallel to $l$.

Q. Draw any line segment $AB$. Mark any point $M$ on it. Through $M$, draw a perpendicular using ruler and compass.

Q. Draw any line segment PQ. take any point R not on it .through R, draw perpendicular to PQ. (use ruler and set - square)

Q. A perpendicular is drawn to a line segment $\overline{MN}$ at N using protractor and point P is marked on perpendicular , then_______ .

1. $\overline{MP}\perp \overline{NP}$
2. $\overline{MN}\parallel \overline{NP}$
3. $\overline{MN}\parallel \overline{MP}$
4. $\overline{MN}\perp \overline{NP}$

Q. If the sum of the distance of point from two perpendicular lines in a plane is $1$, then prove that its locus is a square.

Q. Draw a line segment $PQ=4cm$. Draw a perpendicular bisector to $PQ$

Q. Draw segment ST and KL. Draw segment DE equal in length to the sum of the lengths of these two segments.

Q. Draw any line segment $AB$ and mark any point $P$ on it. Using a ruler and a compass draw a perpendicular on $AB$ through point $P$.

Q. Draw the perpendicular bisector of $XY$, whose length is $10.3$ cm