Two horses are ready to return to their barn after a long workout session at the track. the horses are at coordinates h(1,10) and z(10,1). their barns are located in the same building, which is at coordinates b(-3,-9). each unit/grid on the coordinate plane represents 100 meters. which horse is closer to the barn. justify your answer ?

Horse at Z (1640.1m from barn)

To answer this question you need to determine each horse distance to their barn. For horse H the distance would be 
X: 1-(-3)= 4
Y: 10-(-9)= 19
If you use Pythagoras theory then the distance would be 
BH^2= 4^2 + 19^2
BH^2=  377
BH= 19.416
Horse H is 1941.6m from the barn

For horse Z the distance would be:
X: 10- (-3)= 13
Y:  1-(-9)= 10
BZ^2 = 13^2 + 10^2
BZ^2 = 269 
BZ= 16.401
Horse Z is 1640.1m from barn, a bit closer than horse H