#color(blue)("Assumption: We are looking at the shortest distance between the two Cartesian points.")#

#color(blue)("Which is a strait line.")#

#color(magenta)("However, the" (-7pi)/4"implies Polar Coordinate system. It is not stated that this is the case!!!") #

Ant two points on a strait line graph can be viewed as forming a right triangle. Unless it is of the forms# x=n" or y=p# where n and p are some constant.

So we are looking at #("difference in y-axis")/("difference in x-axis")#

That is #(x_2-x_1)/(y_2-y_1)#

Let #(x_1,y_1)->(-9,17/12)#

Let #(x_2,y_2)->(-2,(-7pi)/4)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Using Pythagoras

Let the distance between the points be d then

#d^2= (x_2-x_1)^2+(y_2-y_1)^2#

#d^2=[color(white)(1/2)(-2)-(-9)]^2+[(-7pi)/4-17/12]^2#

#d^2=7^2+( (17-21pi )/12)^2#

#d=sqrt( 49 + (2398.398)/144)color(white)(...)# to 3 decimal places

#d~~8.103 # to 3 decimal places