A city has two main roads which cross each other at the centre of the city. These two roads are along the North–South (N–S) direction and East–West (E–W) direction. All the other streets of the city run parallel to these roads and are m apart. There are streets in each direction.
Using cm m, draw a model of the city in your notebook. Represent the roads/streets by single lines.
Draw two perpendicular lines intersecting at the center (Origin). Using cm m, draw parallel lines at cm intervals on both sides of the N–S road and parallel lines at cm intervals on both sides of the E–W road.
There are street intersections in the model. Each street intersection is formed by two streets—one running in the N–S direction and another in the E–W direction. Each street intersection is referred to in the following manner: If the second street running in the N–S direction and 5th street in the E–W direction meet at some crossing, then we call this street intersection . Using this convention, find:
(a) how many street intersections can be referred to as .
(b) how many street intersections can be referred to as .
Explanation
The city model represents a 2-D Cartesian coordinate system where the main roads act as the x-axis and y-axis, crossing at the origin .
Because distances to the right and upwards are positive, and distances to the left and downwards are negative, a specific street number (like the 4th street) exists on both the positive and negative sides of the origin.
Therefore, any intersection will have four possible locations in the grid: