Rectangular coordinate*. If - he oodrdi- 



nate axes are rectangular, then cos *- M, ami th. formula 



uce between tin- t\\.i / beootuet 



4 V(| - *;) + (|f i - |f f ) f . . [ J J 



Since either of the t\\ - may U n.n. >is 



may be expressed in words thu 



the 9(fua> mce between two given point* it the yuare 



r abtcittat plue the i<juare of the 

 r ordinate*. 



27. Slope of a line. By the slope of a line is meant the 

 tangent >f the angle whit h tin- line makes with the pour 

 end of the *-axis.' 



I : 'in this .1- -tin ii i. ii it ut once follows that the slope m of 

 the lin- j>in (mint* P\ = (x\* y\) and P?= (^yi) 



ig rectangular, is m = T^-J; that is, 



.= ' '" [=J 



TI 



EXERCISES 



1 stanoM between the poiuU (1,3), (2,7), an.l < I. 1 >, 

 taken in pairs. 



2 I M..1 the dUUneea for the pointa of F.x 1. if the axes are oblique 



oisW. 



3 1'rove that the poinU ( 2.-1). (1,0). (4,3). and (1,2) are the 

 vertices of a parallelogram. 



4 I mce between the pointa (a + 6, c + a) and 

 . 6 + r); also between (a, A) and (-b, -6). 



5 I -111.1 the distances between the points (2, 90). (.% ^\ and 

 "). taken in pairs. 



The slope of a roof or of a hill has the same meaning Thus if 



.( a hill (to the horizontal) is ,| |f it rises S feel vertical in 100 feet 

 horizontal 



AX. OftOM. S 



