Q:

Find the distance betwen the folowing points.a. (4, −9) and (1, −5)b. 4 − 9i and 1 − 5ic. Explain why they have the same answer numericaly in parts (a) and (b) but a diferent perspective ingeometric efect

Accepted Solution

A:
Answera) (4, −9) and (1, −5) distance between two points  [tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]  [tex]D = \sqrt{(1-4)^2+(-5-(-9))^2}[/tex]  [tex]D = \sqrt{9+16}[/tex]         D = 5 b) 4 − 9 i and 1 − 5 i   r = (4-1) + (-9 -(-5))i   r = 3 - 4 i [tex]D = \sqrt{3^2 + 4^2}[/tex] [tex]D = \sqrt{3^2 + 4^2}[/tex] [tex]D = \sqrt{9+16}[/tex] [tex]D = \sqrt{25}[/tex] D = 5c) both the result are numerically same because complex number represent point on the graph where y -axis represent imaginary axis and x -axis is real value axis.