# Locus of the Points Equidistant From Two Intersecting Lines

## Trending Questions

**Q.**The perimeter of the triangle formed by the points (0, 0), (0, 1) and (0, 1) is

(a) 1 ± $\sqrt{2}$

(b) $\sqrt{2}$ + 1

(c) 3

(d) $2+\sqrt{2}$

**Q.**Draw a triangle with sides 5 cm, 6 cm, and 7 cm.

Then draw another triangle whose sides are 45 of the corresponding sides of first triangle.

**Q.**Question 52

To construct a unique rectangle, the minimum number of measurements required is

(a) 4

(b) 3

(c) 2

(d) 1

**Q.**ABCD is a trapezium such that BC || AD and AD = 4 cm. If the diagonals AC and BD intersect at O such that $\frac{\mathrm{AO}}{\mathrm{OC}}=\frac{\mathrm{DO}}{\mathrm{OB}}=\frac{1}{2}$, then BC =

(a) 7 cm

(b) 8 cm

(c) 9 cm

(d) 6 cm

**Q.**X and Y are points of linear on the sides AB and AC respectively of a triangle ABC such that AXAB=14, AY = 2 cm and YC = 6 cm. Find whether XY||BC or not

**Q.**

Draw a square of sides 5 centimetres and draw its circumcircle and incircle.

**Q.**

Using a ruler and compasses only :

(i) Construct a triangle ABC with the following data :

AB = 3.5 cm, BC = 6 cm and ∠ABC=120∘

(ii) In the same diagram draw a cricle with BC as diameter. Find a point P on the circumference of the circle which is equidistant from AB and BC.

(iii) Measure ∠BCP.

**Q.**In Fig. 14.36, a right triangle BOA is given C is the mid-point of the hypotenuse AB. Show that it is equidistant from the vertices O, A and B.

**Q.**If three points (0, 0), $\left(3,\sqrt{3}\right)$ and (3, λ) form an equilateral triangle, then λ =

(a) 2

(b) −3

(c) −4

(d) None of these

**Q.**Question 193

Construct a parallelogram POUR in which PO = 5.5 cm, OU = 7.2 cm and ∠O=70∘.

**Q.**

In a circle of radius 3 cm, construct a chord of length 4 cm. Measure the distance between the centre and the chord.

**Q.**Prove that the points (2, 3), (−4, −6) and (1, 3/2) do not form a triangle.

**Q.**In a △ABC, it is given that AD is the internal bisector of ∠A. If AB = 10 cm, AC = 14 cm and BC = 6 cm, the CD = ?

(a) 4.8 cm

(b) 3.5 cm

(c) 7 cm

(d) 10.5 cm

**Q.**

The locus of a point in a rhombus which is equidistant from any two adjacent sides coincides with the diagonal of that rhombus.

line segment joining them

bisector of line

**Q.**Construct a ∆PQR, in which PQ = 6 cm, QR = 7 cm and PR = 8 cm. Then, construct another triangle whose sides are $\frac{4}{5}$ times the corresponding sides of ∆PQR. [CBSE 2013, 14]

**Q.**

On a graph paper, draw the lines x=3 and y=-5.

Now, on the same graph paper, draw the locus of the point which is equidistant from the given lines.

**Q.**

How do you find the slope of a straight line obtained on a graph?

**Q.**Question 203

Construct a trapezium ABCD, where AB∥CD, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure ∠B and ∠A.

[Hint Difference of two parallel sides gives an equilateral triangle]

**Q.**Question 188

Construct a rhombus whose side is 5 cm and one angle is of 60∘.

**Q.**

The graph of $\mathrm{y}=6$ is a line

**Q.**ABC is a right-angled triangle at B, in which AB = 3 cm and BC = 4 cm, Draw its incircle. [3 MARKS]

**Q.**

Using only ruler and compasses, construct a ΔABC in which BC = 6cm, ∠ABC = 120∘ and AB = 3.5 cm. Now, with BC as diameter, draw a circle. Find a point P on the circumference of the circle such that it is equidistant from AB and BC. Then the measure ∠BCP is

60

^{°}50

^{°}30

^{°}45

^{°}

**Q.**If the bisector of angles A and B of a quadrilateral ABCD intersect each other at the point P. The point P is equidistant from AD and BC.

- True
- False

**Q.**

Can a triangle be constructed with sides of given lengths?

$2,6,4$

**Q.**Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are $\frac{3}{4}$ time the corresponding sides of ΔABC.

**Q.**

To construct a square from a given triangle, we need to make a rectangle of length and breadth equal to ______ and _______ of the triangle.

base, half of height

base, altitude

half of base, height

none of the above

**Q.**

Draw an angle ABC=75o.Find a point P such that P is at a distance of 2 cm from AB and 1.5 cm from BC.

**Q.**

Can a triangle be constructed with sides of given lengths?

$2,3,4$

**Q.**

Draw the graph of y=x2−3x+2

**Q.**Construct a ∆ABC, with BC = 7 cm, $\angle $B = 60º and AB = 6 cm. Construct another triangle whose sides are $\frac{3}{4}$ times the corresponding sides of ∆ABC. [CBSE 2008, 09, 15]