You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Locus of the Points Equidistant From Two Intersecting Lines

Draw two inte...

Question

Draw two intersecting lines to include an angle of 30 $^{\circ}$ . Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such points exist?

3 points

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 points

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1 point

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 points

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
4 points

Draw two intersection lines AB and CD intersection at O such that $∠$ AOC = 30 $^{\circ}$ . Clearly, points equidistant from these lines lie on the bisectors of $∠$ AOC, $∠$ AOD, $∠$ DOB and $∠$ BOC. Draw the bisectors of these angles.

Taking O as centre and radius of 2cm, draw a circle. Clearly, this circle cuts OP, OR, OQ and OS at four points L,M,N and U respectively.

Hence, there are four points which are equidistant from AB and CD and 2 cm away from O.

Suggest Corrections

Similar questions

Draw two intersecting lines to include an angle of 30 $^{\circ}$ . Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such point/points exist(s)?

Draw an equilateral ∆ of side 4.5 cm & construct all its lines of symmetry

a) How many lines of symmetry are present in the equilateral ∆

b) How many points of symmetry are present in the equilateral ∆

Q. The steps of construction of an

∠ A O B = 45^{o}

is given in jumbled order below:
1. Place compass on intersection point.
2. Place ruler on start point and where arc intersects perpendicular line.
3. Adjust compass width to reach start point.
4. Construct a perpendicular line.
5. Draw

45

degree line.
6. Draw an arc that intersects perpendicular line.
Which step comes first?

Q. Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown.
Construct a

△ A B C

in which

B C = 6.5 c m, ∠ A B C = 60^{\circ}, A B = 5 c m

. Construct a locus of points

l_{1}

at a distance of

3.5 c m

from

A

. Also, construct a locus of points

l_{2}

which is equidistant from

A C

and

B C

. Let

l_{1}

intersect

l_{2}

in two points

X

and

Y

. Measure

X Y

Mention the proper order of identifying a point D on BC such that $\frac{B D}{D C} = \frac{2}{3}$ .
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.

Join BYJU'S Learning Program

Draw two intersecting lines to include an angle of 30∘. Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such points exist?

Draw two intersecting lines to include an angle of 30 $^{\circ}$ . Use ruler and compass to locate points which are equidistant from these lines and also 2 cm away from their point of intersection. How many such points exist?