Every Point on the Perpendicular Bisector of a Segment Is Equidistant from the End Points of the Segment

Q.

Construct a triangle of sides$4\mathrm{cm},5\mathrm{cm},\mathrm{and}6\mathrm{cm}$ and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle. Give the justification for the construction

Q.

Use graph paper for this question. Take 1 cm = 1 unit on both axes.

(i) Plot the points A(2, 2), B(6, 4) and C(3, 6).

(ii) Construct the locus of points equidistant from A and B.

(iii) Construct the locus of points equidistant from AB and AC.

(iv) Locate the point P such that PA = PB and P is equidistant from AB and AC.

Then the length(approximately) of PA in cm is

1. 2.5 cm

2. 1.5 cm

3. 4 cm

4. 3.5 cm

Q.

The bisectors of angle A and C of a quadrilateral ABCD intersect each other at P. Then P is equidistant from the opposite sides AB and CD.

1. True

2. False

Q.

In the above triangle ABC, AB = BC. BD is perpendicular to AC and EC bisects the angle $\angle ACB$. Which of the following is correct?

1. E is equidistant from AC and BC.

2. Both option(a) and option (b) are correct.

3. P is equidistant from points A and C

4. Both option(a) and option (b) are wrong.

Q.

On constructing a triangle ABC, with AB = 5.6 cm, AC = BC = 9.2 cm, the distance between the points which are both equidistant from AB and AC and also 2 cm from BC is

1. 4 cm

2. 4.4 cm

3. 4.2 cm

4. 4.3 cm