Locus of the Points Equidistant From Two Intersecting Lines

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 $\frac{4}{5}$ 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 $\frac{AX}{AB}=\frac{1}{4}$, 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 $\angle ABC={120}^{\circ }$

(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 $\angle BCP.$

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 $\angle O={70}^{\circ }$.

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.

1. line segment joining them

2. 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 $AB\parallel CD$, AD = BC = 3.2 cm, AB = 6.4 cm and CD = 9.6 cm. Measure $\angle B$ and $\angle A$.

[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 ${60}^{\circ }$.

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 $\Delta$ABC in which BC = 6cm, $\angle$ABC = 120${}^{\circ }$ 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 $\angle$BCP is

1. 60^°

2. 50^°

3. 30^°

4. 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.

1. True
2. 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.

1. base, half of height

2. base, altitude

3. half of base, height

4. none of the above

Q.

Draw an angle ABC=${75}^o$.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 $y=x^2-3x+2$

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]