color(blue)("Assumption: We are looking at the shortest distance between the two Cartesian points.")Assumption: We are looking at the shortest distance between the two Cartesian points.
color(blue)("Which is a strait line.")Which is a strait line.
color(magenta)("However, the" (-7pi)/4"implies Polar Coordinate system. It is not stated that this is the case!!!") However, the−7π4implies 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=px=nory=p where n and p are some constant.
So we are looking at ("difference in y-axis")/("difference in x-axis")difference in y-axisdifference in x-axis
That is (x_2-x_1)/(y_2-y_1)x2−x1y2−y1
Let (x_1,y_1)->(-9,17/12)(x1,y1)→(−9,1712)
Let (x_2,y_2)->(-2,(-7pi)/4)(x2,y2)→(−2,−7π4)
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Using Pythagoras
Let the distance between the points be d then
d^2= (x_2-x_1)^2+(y_2-y_1)^2d2=(x2−x1)2+(y2−y1)2
d^2=[color(white)(1/2)(-2)-(-9)]^2+[(-7pi)/4-17/12]^2d2=[12(−2)−(−9)]2+[−7π4−1712]2
d^2=7^2+( (17-21pi )/12)^2d2=72+(17−21π12)2
d=sqrt( 49 + (2398.398)/144)color(white)(...) to 3 decimal places
d~~8.103 to 3 decimal places
