Question #040c8

2 Answers
Feb 18, 2017

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.

Feb 18, 2017

#(-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"#