Mathematics, 18.07.2019 03:30, jonmorton159

Triangle abc has vertices a(0 0) b(6 8) and c(8 4). which equation represents the perpendicular bisector of bc

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answered: AdrianBrewer8168

The equation of the perpendicular bisector of line BC is :

$y=\frac{1}{2}x+\frac{5}{2}$

The given coordinates are:

A(0, 0), B(6, 8), C(8, 4)

Find the midpoint of line BC

$x=\frac{x_1+x_2}{2} \\\\x=\frac{6+8}{2} \\\\x=7\\\\\\y=\frac{y_1+y_2}{2} \\\\y=\frac{8+4}{2} \\\\y=6$

The coordinate of the midpoint of line BC is (7, 6)

Find the slope of line BC

$m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{4-8}{8-6} \\\\m=-2$

The equation of the perpendicular bisector of BC is:

$y=\frac{-1}{m}x+b\\\\$

Solve for the y-intercept, b

$6=\frac{-1}{-2}(7)+b \\\\12=7+2b\\\\2b=12-7\\\\b=5/2$

The equation of the perpendicular bisector of line BC is therefore:

$y=\frac{1}{2}x+\frac{5}{2}$

Learn more on perpendicular bisector here: link

answered: mckenziebeach5ox9oy3

Perpendicular means that the slope of one line is the opposite reciprocal of the other; bisector means that the line that is perpendicular is cutting the other one exactly in half. So we have to find 2 things about BC: the first is the midpoint which will then serve as the x and y coordinates in our new equation, and second is the slope of it. First things first: the midpoint formula is this: $M=( \frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} )$ . Using our coordinates we fill in that formula like this: $M=( \frac{6+8}{2}, \frac{8+4}{2} )$ which of course gives us a midpoint of (7, 6). Now for the slope of the line BC: $m= \frac{4-8}{8-6} =-2$ . But since we need the perpendicular slope of that we will take its opposite reciprocal which is 1/2. Now use the x and y coordinates of the midpoint and that newly found slope and write your equation to solve for b. $6= \frac{1}{2}(7)+b$ . Solving that for b gives you that b = 5/2. So the equation of the line that is the perpendicular bisector of BC (drum roll, please...) is $y= \frac{1}{2} x+ \frac{5}{2}$

answered: Guest

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