Posted by **jigna** on Sunday, February 25, 2007 at 6:41am.

A straight road separates towns A (grid ref 42,45) and B (grid ref 52,40) A village is situated at grid ref (46,57) and a new road is planned from the village to road AB. What is the shortest road possible (1 dp)

Please define an origin and a set of axes

Use Cartesian geometry principles to work out lenght of the shortest line

The shortest route to the road would be perpendicular to the road.

The origin of coordinates has already been designated as where the grid is (0,0). The axis have also been defined as the map grid.

The "slope" of the road on the map from A to B, relative to the x axis, is

(40-45)/(52-42) = -1/2.

That means the slope (direction) of the line from the village at (46,57) to road AB is +2 (since it is perpendicular to AB).

The equation for the new road is

y - 57 = 2(x - 46)

y = 2x - 35

The roads connect where the equation of the AB road is also valid:

(y - 45) = (-1/2) (x - 42)

y = -(1/2)x + 66

Solve the two equations:

0 = 2.5 x - 101

x = 40.4

y = 45.8

Shortest new road length =

sqrt[(46 - 40.4)^2 + (57 - 45.8)^2]

= 12.52

Check the math; the method should be OK. Also try plotting it on graph paper to see if it makes sense.

## Answer this Question

## Related Questions

geometry - When finding the perimeter of a figure on a grid,whydo you not count ...

math - draw a 5cm x 5cm grid in your homework book. your task is to break the ...

Math - Ms wanton recycles colored pencils in a box for use in her art class. She...

chemistry ap ...urgent! please help me! - The measurement of pH using a glass ...

Math - There is a 4 by 4 grid of points. Each pair of horizontally adjacent or ...

geometry - The simplests example of a magic square is a 3 by 3 grid. The tasks ...

Math - When finding the perimeter of the figure on a grid why do you not count ...

Math - When finding the perimeter of a figure on a grid, why do you not count ...

electricity - The grid in a high-vacuum triode is usually kept negatively ...

MATH - A four by four grid of unit squares contains squares of various sizes (1 ...