Find an equation for the line passing through the point that is perpendicular to the line passing through and .
A) y = x
B) y = x
C) y = x
D) y = x
E) y = 5 x

Question

Find an equation for the line passing through the point  that is perpendicular to the line passing through  and  .
A) y = x 
B) y = x 
C) y = x 
D) y = x 
E) y = 5 x

Quizplus · Accepted Answer

Let's first find the slope of the given line.
Slope of the line passing through (11ec19db_8483_4419_9dbe_f3e5d8cc9495_TBX8673_11, 11ec19db_8483_441a_9dbe_dfbf1cc8f88e_TBX8673_11)  and (11ec19db_8483_441a_9dbe_dfbf1cc8f88e_TBX8673_11,11ec19db_8483_4418_9dbe_89f7cf793f26_TBX8673_11) is:
m = (11ec19db_8483_4418_9dbe_89f7cf793f26_TBX8673_11 - 11ec19db_8483_441a_9dbe_dfbf1cc8f88e_TBX8673_11)/(11ec19db_8483_441a_9dbe_dfbf1cc8f88e_TBX8673_11 - 11ec19db_8483_4419_9dbe_f3e5d8cc9495_TBX8673_11)
m = -2

The line perpendicular to this line will have slope = 1/2 (negative reciprocal)
Let (x, y) be any point on the line we want to find. We know it passes through (11ec19db_8483_4418_9dbe_89f7cf793f26_TBX8673_11, y1)
Using point-slope form, 
(y1 - y) = 1/2(11ec19db_8483_4418_9dbe_89f7cf793f26_TBX8673_11 - x)
y = 11ec19db_8483_6b30_9dbe_336aec9830f9_TBX8673_11 + 1/2x
Therefore, the correct choice is D.

Find an Equation for the Line Passing Through the Point