Question

Find, in terms of x and y , the equation of the perpendicular bisector of the line segment joining the points(-1,2) and (-7,0) . The equation of the perpendicular bisector is .?

Answer 1

`y=-3x-11`

Explanation:

`"the perpendicular bisector, bisects the segment at "`
`"right angles"`

`"mid-point "=[1/2(-1+(-7)),1/2(2+0)]`

`color(white)(xxxxxxxx)=(-4,1)`

`"given a line with slope m then the slope of a line "`
`"perpendicular to it is"`

`m_(color(red)"perpendicular")=-1/m`

`" calculate the slope m using the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(-1,2)" and "(x_2,y_2)=(-7,0)`

`rArrm=(0-2)/(-7-(-1))=(-2)/(-6)=1/3`

`rArrm_(color(red)"perpendicular")=-1/(1/3)=-3`

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`rArry=-3x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-4,1)" into the partial equation"`

`1=12+brArrb=-11`

`"equation of perpendicular bisector is"`

`y=-3x-11larrcolor(red)"in slope-intercept form"`