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s2008m [1.1K]
3 years ago
8

Write the equation of the perpendicular bisector of . Point B is located at (–3, 1), and point C is located at (1, 5).

Mathematics
1 answer:
maxonik [38]3 years ago
6 0

The equation of perpendicular bisector of BC is

y=-x+2

Further explanation:

A perpendicular bisector passes through the mid-point of a line so to get an ordered pair from which the perpendicular bisector will pass we need to find the mid-point of BC.

Mid-point = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2} )\\Here\\(x_1,y_1) = (-3,1)\\(x_2,y_2) = (1,5)\\Putting\ values\ in\ formula\\M = (\frac{-3+1}{2} , \frac{1+5}{2} )\\= (\frac{-2}{2} ,\frac{6}{2})\\= (-1, 3)

So the perpendicular bisector will pass through (-1,3)

Let m1 be the slope of BC

Then

m_1 = \frac{y_2-y_1}{x_2-x_1} \\=\frac{5-1}{1+3} \\=\frac{4}{4}\\ =1

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of perpendicular lines is -1.

m_1.m_2 = -1\\1*m_2 = -1\\m_2 = -1

The standard form of point-slope form of line is:

y=mx+b

Putting the value of slope of bisector we get

y=(-1)(x)+b\\y=-x+b

To find the value of b, put the ordered pair (-1,3) in the equation

3 = -(-1) +b\\3= 1+b\\3-1 =b\\b=2\\

Putting the values of m and b in standard form

y=-x+2

Hence the equation of perpendicular bisector of BC is

y=-x+2

Keywords: Perpendicular bisector, Point-slope form

Learn more about point-slope form at:

  • brainly.com/question/7490805
  • brainly.com/question/8358304

#LearnwithBrainly

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