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04 Apr 2020, 02:09
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D
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If the coordinates of point A are (2,2) and the coordinates of point B are (0,-2), what is the equation of the perpendicular bisector of line segment AB?
(A) y = 1/2x + b
(B) y = -1/2x + b
(C) y = 2x + 3/2
(D) y = -1/2x + 1/2
(E) y = 3/2x - 1/2
(A) y = 1/2x + b
(B) y = -1/2x + b
(C) y = 2x + 3/2
(D) y = -1/2x + 1/2
(E) y = 3/2x - 1/2
reynaldreni
Joined: 07 May 2015
Last visit: 02 Nov 2022
Posts: 73
Given Kudos: 152
Location: India
Schools: Darden '21
GPA: 4
10 Sep 2020, 07:54
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Vidit17
Hi Vidit17 ,
To find the perpendicular bisector of a line, first find the mid-point. Here in the problem we need to find the mid-point of (2,2) and (0,-2)
Midpoint = (2+0/2 , 2-2/2) = (1,0)
The perpendicular bisector has the slope which is -1/m; from the problem we know slope of the line is 2; so the slope of perpendicular bisector is -1/2
So the equation of the perpendicular bisector is y = -1/2x + b
since the line passes through the mid-point (1,0) we can substitute this value and find the value of b
hence we get 0 = -1/2(1) + b ; b = 1/2
we re-write the equation of the perpendicular bisector as y = -1/2x + 1/2 (D)
You may read more in the URL : https://socratic.org/questions/how-do-you-find-the-equation-of-the-perpendicular-bisector-of-the-points-1-4-and
04 Apr 2020, 08:27
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Given Points are A (2,2); B (0,-2)
Midpoint of AB is (1,0)
Slope of AB is
{ - 2 - 2}/{0 - 2} = { - 4}/{ - 2} = 2
Slope of Perpendicular Bisector is
= { - 1}/{slope of AB} = { -1}/{2}
Equation of Perpendicular Bisector is
y - 0 = { - 1}/{2} )(x - 1)
or,y= -1/2x+1/2
correct answer is D
Midpoint of AB is (1,0)
Slope of AB is
{ - 2 - 2}/{0 - 2} = { - 4}/{ - 2} = 2
Slope of Perpendicular Bisector is
= { - 1}/{slope of AB} = { -1}/{2}
Equation of Perpendicular Bisector is
y - 0 = { - 1}/{2} )(x - 1)
or,y= -1/2x+1/2
correct answer is D
