on a number line the cordinates of x,y,z, and w are -8, -5, 2, and 5, respectively. find the lenght of two segments below then tell weather they are congruent?

Question

On a number line, the cordinates of x, y, z, and w are -8, -5, 2, and 5, reapectively. Find the legth of the two segments below. Then tell wether they are confruent.

 

Answer 1

The table below shows the lengths of all possible segments. To find the distance between two coordinates, we find out where the column of one meets the row of the other. For example, WX (which is the same as XW) is the difference between 5 and -8: take the smaller from the larger: 5-(-8)=5+8=13, so where the row and column meet there is 13. Ignore the cells containing * because that is the distance from the point on to itself.

 

           W(5)  X(-8)  Y(-5)  Z(2)

W(5)      *        13       10         3

X(-8)      13      *          3        10

Y(-5)      10      3         *          7

Z(2)         3     10         7         *

 

There are 4 different distances: 3, 7, 10, 13.

3 is WZ, XY, YX and ZW

7 is YZ and ZY

10 is WY, XZ, YW and ZX

13 is WX and XW

 

So two segments are 3 units apart and two segments are 10 units apart.

Therefore WZ=XY and WY=XZ.