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goblinko [34]
2 years ago
5

Please help!!!

Mathematics
1 answer:
stealth61 [152]2 years ago
6 0

Answer:

y-1=\frac{1}{8}\left(x-7\right) is the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).

Step-by-step explanation:

The endpoints:

  • B(6,9)
  • C(8,−7)

Calculating the Midpoint M of BC:

\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)

\left(x_1,\:y_1\right)=\left(6,\:9\right),\:\left(x_2,\:y_2\right)=\left(8,\:-7\right)

The Midpoint M of BC =\left(\frac{8+6}{2},\:\frac{-7+9}{2}\right)

                                     =\left(7,\:1\right)

Calculating the slope of BC:

\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(6,\:9\right),\:\left(x_2,\:y_2\right)=\left(8,\:-7\right)

m=\frac{-7-9}{8-6}

m=-8

Given a line with slope m then the slope of a

line  perpendicular to it is:

m_{prependicular}=-\frac{1}{m}=-\frac{1}{-8}=\frac{1}{8}

Equation of line using point-slope form

y-y_1=m\left(x-x_1\right)

y-1=\frac{1}{8}\left(x-7\right)        

     

Therefore, y-1=\frac{1}{8}\left(x-7\right) is the equation in point-slope form for the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7).                                          

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