Question

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

(i) Plot the points A(1, 1), B(5, 3) and C(2, 7).

(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

Answer 1

Take 1 cm = 1 unit on both axes.

(i) Plot the given points A(1, 1), B(5, 3) and C(2,7).

(ii) Construct the perpendicular bisector of AB.

(We know that the locus of a point which is equidistant from two fixed points is the perpendicular bisector of the line segment joining the two fixed points. So, we construct the perpendicular bisector of AB).

(iii) Construct the bisector of $\angle BAC$.

(We know that the locus of a point which is equidistant from two intersecting straight lines is a pair of straight lines which bisect the angles between the given lines. So, we construct the bisector for angle A).

(iv) P is the point of intersection of the perpendicular bisector of the line segment AB and the bisector of $\angle BAC$.

On measuring, we get, length of PA = 2.5 cm approx.