Indicate the equation of the line that is the perpendicular bisector of the segment with endpoints (4, 1) and (2, -5).

Question

anonymous · Answer

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campbell_st · Answer

start by finding the slope of the line joining the 2 points... and also find the midpoint of the segment

anonymous · Answer

The slope is 3 right?

anonymous · Answer

And the midpoints are 3, -2 right?

campbell_st · Answer

slope is correct... and midpoint is correct. 

so you need to find the negative reciprocal of the slope

because the product the the slope of a line and a perpendicular must be -1

so the slope of the perpendicular is 

m = -1/3

so the equation of the line is 

$$y = - \frac{1}{3} x+ b$$

just substitute the x and y values from the midpoint to find b. 

hope it helps

anonymous · Answer

I dont get it :( I need to get the answer without any fractions

campbell_st · Answer

well then multiply every term in the equation by the denominator of the fraction... 

so what value did you get for b..?

anonymous · Answer

how do I get b??

campbell_st · Answer

your midpoint is (3, -2) 

so x = 3 and y = -2 

substitute them into 

$$y = -\frac{1}{3} x + b$$

what do you get..?

anonymous · Answer

is it -1?

campbell_st · Answer

well 

that's correct so the equation is 

$$y = -\frac{1}{3} x - 1$$

if you don't like the fraction multiply each term by 3

campbell_st · Answer

the equation can be 

3y = -x - 3

or

x + 3y = -3

anonymous · Answer

if I multiply by 3..what would I get? would it be x+y=-3?

anonymous · Answer

but it wont fit my answer table. |dw:1410329048705:dw|