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

Question

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)

sjavvadi · Accepted Answer

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).

GMATinsight · Answer

Please find the explanation as attached.

Bunuel · Answer

Draw y = - 2 x + 6 and use the options. Similar questions: in-the-rectangular-coordinate-system-above-the-line-y-x-144774.html in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html the-line-represented-by-the-equation-y-4-2x-is-the-127770.html

daveglasgow · Answer

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?

(-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!

Nunuboy1994 · Answer

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

NabilSaleem · Answer

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

Adarsh_24 · Answer

In case someone finds it helpful.
I have gone through multiple questions like this here.

my take away is to try not to expand the (a-b)^2
we have y=(x-3)/2
also
20= (x-3)^2+y^2
then
20=(x-3)^2 +(x-3)^2 / 4
so we can easily take out (x-3)^2.
20=(x-3)^2 * 5/4

finisher009 · Answer

Step-by-Step Solution:

1. Find the Slope of the Perpendicular Line: The given line is `y = -2x + 6`. The slope of this line is -2. The slope of the line segment `AB` must be the negative reciprocal of -2.
 • Negative reciprocal of -2 is `-1 / (-2) = 1/2`.

2. Test the Answer Choices: Now, calculate the slope between point `A (7, 2)` and each answer choice. The correct answer must give a slope of `1/2`. Let’s use the formula: `slope = (y2 - y1) / (x2 - x1)`.
 • A. (-2, -1): slope = `(-1 - 2) / (-2 - 7)` = `-3 / -9` = `1/3`. Incorrect.
 • B. (-1, -2): slope = `(-2 - 2) / (-1 - 7)` = `-4 / -8` = `1/2`. This matches. This is our answer.
 • C. (-2, 1): slope = `(1 - 2) / (-2 - 7)` = `-1 / -9` = `1/9`. Incorrect.
 • D. (-1, 2): slope = `(2 - 2) / (-1 - 7)` = `0 / -8` = `0`. Incorrect.
 • E. (7, 2): This is the same as point A. Incorrect.

We found the answer in two quick steps by focusing on the “perpendicular” property. There is no need to even check the “bisector” (midpoint) property, as only one answer choice works.

The correct answer is B. (-1, -2).

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

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

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