Maths 3 Mark Question

Take a rectangular sheet of paper. Fold the paper so that the lower edge of the paper falls on its top edge, and fold it over again from right to left. Observe the two folds that have formed on the . paper. Verify that each fold is a perpendicular bisector of the other. Then measure the following distances. (Textbook pg. no. 91)
i. l(XP)
ii. l(XA)
iii. l(XB)
iv. l(YP)
v. l(YA)

You will observe that l(XP) = l(YP), l(XA) = l(YA) and l(XB) = l(YB)
Therefore we can conclude that all points on the vertical fold (perpendicular bisector) are equidistant from the endpoints of the horizontal fold.

The Perpendicular Bisector.

1. A wooden ‘yoke’ is used for pulling a bullock cart. How is the position of the yoke determined?
2. To do that, a rope is used to measure equal distances from the spine/midline of the bullock cart. Which geometrical property is used here?
3. Find out from the craftsmen or from other experienced persons, why this is done.

In the above construction, why must the distance in the compass be kept constant?

Draw line CD. Take any point M on the line. Using a protractor, draw a line perpendicular to line CD at the point M.

Draw a line AB. Using a compass, draw a line perpendicular to AB at point B.

Draw line l. Take any point P on the line. Using a set square, draw a line perpendicular to line l at the point P.