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Answer 1 · 2017-06-10T13:26:20

#2sqrt(10)" "# as an exact value

When 'reading' a graph in '2-space' (x and y axis) then you always read left to right on the x-axis

Let point 1 be #P_1->(x_1,y_1)=(-1,-3)#
Let point 2 be #P_2->(x_2,y_2)=(1,3)#
Let the direct distance from #P_1" to "P_2# be #d#

The link between Pythagoras and the distance between two points is due to the triangle depicted in the graph below:

Tony B

Thus we have: #d^2=(x_2-x_1)^2+(y_2-y_1)^2#

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

#=> d=sqrt([1-(-1)]^2+[3-(-3)]^2)#

#d=sqrt(4+36)" "=sqrt(40)#

#d=sqrt(2^2xx10)" "=2sqrt(10)" "# as an exact value