# Question #a7d14

Feb 8, 2017

As explained below. Distance would be7 cms

#### Explanation:

Draw the line segment AB first. Then with A as center draw arcs of radius 4.2 cms on either side of line AB. Similarly draw arcs with radius 5.6 cms with B as center. The two arcs will intersect at one point on either side. On the other side of AB, let the point be named as P'.

These are the required two positions of point P. Measure the distance using a straight edge.

As would be seen the line joining the two positions would be line perpendicular to line AB .

A right angle will be formed at P and also at P'. This is also verified by Pythagoras theorem because $\sqrt{{4.2}^{2} + {5.6}^{2}} = \sqrt{49} = 7$

Thus APBP' being a parallelogram with a pair of opposite angles being right angles, would be rectangle. One diagonal of this rectangle is AB= 7cms, therefore other diagonal PP' would also be 7cms.