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The line represented by the equation y = - 2 x + 6 is

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jlgdr
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The line represented by the equation y = - 2 x + 6 is [#permalink] New post  20 Sep 2013, 16:17
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The line represented by the equation y = -2 x + 6 is the perpendicular bisector of the line segment AB. If A has the coordinates (7,2), what are the coordinates for B?

A. (-2, -1)
B. (-1, -2)
C. (-2, 1)
D. (-1, 2)
E. (7, 2)
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sjavvadi
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  22 Nov 2016, 15:26
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Given y = -2x+6 ---(1)

So slope = -2.

Slope of perpendicular line = 1/2. So equation of line is y=1/2x+C. substitute A(7,2) we get C = -3/2.

Therefore perpendicular line is y=1/2x-3/2----(2)

Solve (1) and (2) for x and y. 1/2x-3/2 = -2x+6 =>5/2x = 25/2 => x = 3. therefor y= 0 i.e. Point of interesection say O = (3,0)

Let point B be (m,n). Since O is hte mid point of A and B -> (m+7)/2 = 3 and (n+2)/2 = 0 => m= -1 and n=-2. Therefore B = (-1,-2).
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  26 Jun 2015, 22:53
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daveglasgow wrote:
Hey guys,

This might be an easy question for some - but I'm struggling to understand it.

The line represented by the equation y = -2x + 6 is the perpendicular bisector of the line segment AB. If A has coordinates (7,2), what are the coordinates for B?



Would it be easier to set this out on a graph?

Thanks in advance!


Please find the explanation as attached.
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  20 Sep 2013, 16:53
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jlgdr wrote:
The line represented by the equation y = - 2 x + 6 is the perpendicular bisector of the line segment AB. If A has the coordinates (7,2), what are the coordinates for B?


Draw y = - 2 x + 6 and use the options.

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daveglasgow
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  26 Jun 2015, 16:03
Hey guys,

This might be an easy question for some - but I'm struggling to understand it.

The line represented by the equation y = -2x + 6 is the perpendicular bisector of the line segment AB. If A has coordinates (7,2), what are the coordinates for B?

Show Spoiler
(-1,-2) If y= -2x + 6 is the perpendicular bisector of the segment AB, then the line containing segment AB must have a slop of 0.5 (the negative inverse of -2)

Question: - Why is the negative inverse of -2 0.5? I have it in my head that it is because opposite of 2/1 is 1/2 which is 0.5?.

Therefore you can represent this line with the equation y = 0.5x + b. Substitute the coordinates (7,2) into the equation to find the value of b.

2 = 0.5(7) + b
b = -1.5

Question: - Why does this equal -1.5? 0.5 x 7 = 3.5 / 2 = 1.75 ?

The line containing AB is y = 0.5 x - 1.5

Find the point at which the perpendicular bisector intersect AB by setting the two equations y = -x + 6 and y = 0.5x - 1.5x equal to each other.

-2x + 6 = 0.5x - 1.5
2.5 x = 7.5
x = 3, y = 0

The two lines intersect at (3,0) which is midpoint of AB.

X Y
A 7 2
MID 3 0
B -1 -2


Would it be easier to set this out on a graph?

Thanks in advance!
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  14 Jun 2017, 19:26
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jlgdr wrote:
The line represented by the equation y = - 2 x + 6 is the perpendicular bisector of the line segment AB. If A has the coordinates (7,2), what are the coordinates for B?


To solve this question you have to know the property of a perpendicular line's slope relative to the slope of the line it passes through- the slope of a perpendicular line is both the opposite (negative if other slope is positive and positive if other slope is negative) and reciprocal (the perpendicular of the slope 2x is 1/2 and 3/2x would be 2/3x).

The slope of the perpendicular line would just be

y= 1/2 x + c( c just represents the y intercept in an equation) now insert the given coordinates
2= 7/2 + c
c = -3/2

Set the two equations equal

1/2x -3/2 = -2x + 6
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  22 Jan 2021, 10:04
Formula needed to solve:
pick slope from y= mx+c where m is slope

perpendicular line = m1*m2 = -1, where m1 & m2 are slopes of perpendicular lines

Apply slope and point A to y = mx+c to find intercept point and form eqn of line AB

now solve line eqn of perpendicular line & AB to find bisector point

then apply mid point to formula m=(mid point of x, mid point of y)

mid point of x = X1+X2/2

mid point of y = Y1+Y2/2
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink] New post  01 Oct 2023, 09:28
GMATinsight wrote:
daveglasgow wrote:
Hey guys,

This might be an easy question for some - but I'm struggling to understand it.

The line represented by the equation y = -2x + 6 is the perpendicular bisector of the line segment AB. If A has coordinates (7,2), what are the coordinates for B?



Would it be easier to set this out on a graph?

Thanks in advance!


Please find the explanation as attached.


Can you please explain how you made the x, y pairs? For example, why can't we pair -1, 2 together and use that as the answer?
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Re: The line represented by the equation y = - 2 x + 6 is [#permalink]
01 Oct 2023, 09:28
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