Not sure how to do this question

Question

Map shows a pipeline going straight from A(45,60) to B(65,40).How long is it if each unit ok the map =1km.Also, what are the coordinates halfway between A & B

Answer 1

After you plot this on an x-y plot and find the distance, remember it.  You will find that three triangles appear an awful lot in algebra, geometry, and trigonometry because they have what I call "magic numbers"  -- values that make the math easy so the student can concentrate on the problem.
 
Here they are:
           angles             sides          
          45-45-90          n*1, n*1, n*SQRT(2)
          30-60-90          n*1, n"*SQRT(3), n*2
         (learn later)       n*3, n*4, n*5
Learn these three because you will see them often:
 
Now, to the problem.
   The distance in the x direction is  | (65) - (45) |  =  20
   The distance in the y direction is  | (40) - (60) |  =  20
  What is the other distance (the hypotenuse)?
 
Hmm... looks like 20*SQRT(2), but let's calculate-
   C^2 = A^2 + B^2
   C^2 = 20^2 + 20^2
   C^2 = 800
    C  = SQRT(800)    (note:  ignore -SQRT(800) since distance is positive)
    C  = SQRT(400)*SQRT(2)
    C  = 20*SQRT(2)  km             yep.

 

Now, the point half-way between the two given points has an x value that is the average of the two x values and has a y value that is the average of the two y values.

 

   So,  the point is  (  (65+45)/2,  (40+60)/2 )

                            (  110/2,     100/2  )

                               (55, 50) is halfway between (45,60) and (65,40)

Answer 2

Jess,

 

This is a bit difficult to answer in text, but let's give it a shot.

 

The easiest way to do this is to make a right triangle using A and B as vertices.

1. Draw a line from A to B.

2. Draw a line straight down from A (45,60) so that it is on the same level horizontally from B. This should give you a line from A to the point (45,40). We'll call this point C.

3. Draw a line directly left from B to C.

 

This should leave you with a right triangle with two sides of known length. AC is 20 in length. BC is 20 in length. Since we have a right triangle, we use the Pythagorean Theorum: a² + b² = c². In this case, a = AC, b = BC, and c = AB.

So AB = √(20²+20²) or 20√2 which is approximately 28.3.

 

Since the map has one unit = 1 km, and the line is 28.3 units long, the distance of the pipeline is 28.3km.

 

To find the halfway points, find the halfway points on each axis separately.

For the x-axis: halfway between 65 and 45 is (65+45)/2, or 55.

Similarly for the y-axis: halfway between 60 and 40 is (60+40)/2 or 50.

 

Therefore the halfway point is (55,50).

 

I hope that helps and good luck!

 

Danny