Monday

April 21, 2014

April 21, 2014

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

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.

**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...

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

math - how do you graph 0.04 on a grid sheet with counting squares in the ...

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

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

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

physics - A beam of electromagnetic waves of a wavelength 3.0cm is directed ...

math - suppose each side of a square in the grid is 4 cenimeters and represents ...