A city has two main roads meeting at center. These two roads are along...
Mathematical Concept Used
The mathematical concept used to solve this problem is Coordinate Geometry.
Explanation
Coordinate Geometry is a branch of mathematics that deals with the study of geometric figures using coordinates. It involves the use of algebraic equations to describe the properties of geometric shapes, such as lines, curves, and surfaces.
In this problem, we can use Coordinate Geometry to determine the location of the cross streets in the city. We can assign coordinates to the intersection of the two main roads, with the north-south road representing the y-axis and the east-west road representing the x-axis.
We can then use the equation for a line to determine the location of each cross street. For example, if we want to find the location of a cross street that is 600 meters north and 900 meters east of the intersection of the two main roads, we can use the equation:
y = mx + b
where m is the slope of the line and b is the y-intercept. In this case, the slope m is 300/300 = 1, since the streets are 300 meters apart in both directions. The y-intercept b is the y-coordinate of the intersection of the two main roads, which we have assigned a value of 0.
So the equation for the line passing through the intersection and the point (900, 600) is:
y = x + 0
which simplifies to:
y = x
This means that the cross street is located at the point (900, 600), which is 900 meters east and 600 meters north of the intersection.
By using this method, we can determine the location of any cross street in the city, given its distance from the intersection of the two main roads.