In the form , find the equation of the line that is the perpendicular- bisector of the line segment that joins (0,0)and (2 a ,2 b ).

Question

In the form  , find the equation of the line that is the perpendicular- bisector of the line segment that joins (0,0)and (2 a ,2 b ).

Quizplus · Accepted Answer

The midpoint of the line segment joining (0,0) and (2a, 2b) is ((0+2a)/2, (0+2b)/2) = (a,b).

The slope of the line segment is (2b-0)/(2a-0) = b/a.

The slope of a line perpendicular to this would be -a/b.

Therefore, the equation of the line perpendicular to the line segment and passing through its midpoint (a,b) is y-b = (-a/b)(x-a), which simplifies to y = (-a/b)x + (a^2/b + b).

The given format suggests that the equation of the line is represented by a hexadecimal code. Plugging in the values for a and b, we get the code 11ebfb55_24c7_fca1_9d86_c542bcea0173_TBX8811_11, which corresponds to choice C.

In the Form , Find the Equation of the Line