Question

Question #040c8

Answer 1

See the Explanation.

Explanation:

Use the Slope-Point Form to find the eqn. of reqd. line (which is,

the Perpendicular Bisector of the Line Segment AB ), to get,

`y-6=2{x-(-1)}, i.e., y=2x+2+6=2x+8.`

Now, try to find out where you have committed mistake.

Answer 2

`(-1,6)" and " y=2x+8`

Explanation:

The coordinates of the midpoint are the `color(blue)"average"` of the x and y coordinates of A and B.

`rArrM=[1/2(1-3),1/2(5+7)]=(-1,6)`

We require to calculate the slope( m ) of AB 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)|)))`
where `(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

The 2 points here are A(1 ,5) and B(-3 ,7)

let `(x_1,y_1)=(1,5)" and " (x_2,y_2)=(-3,7)`

`rArrm_(AB)=(7-5)/(-3-1)=2/(-4)=-1/2`

The slope of a line perpendicular to AB is `color(blue)"the negative inverse"` of the slope of AB.

`rArrm_("perp")=-1/(m_(AB)`

`rArrm_("perp")=-1/(-1/2)=2`

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))`
where `(x_1,y_1)" are the coordinates of a point on the line"`

`"here "m_("perp")=2" and " (x_1,y_1)=M(-1,6)`

`rArry-6=2(x+1)`

distributing and simplifying.

`y=2x+2+6`

`rArry=2x+8" is equation of perpendicular line"`