In the coordinate geometry plane, point A is the midpoint between poin

Question

In the coordinate geometry plane, point A is the midpoint between points (5,8) and (-3, -2). If the midpoint between point A and point B is (4, -1), in which quadrant does point B lie?

A. I
B. II
C. III
D. IV
E. None of the above

BrentGMATPrepNow · Accepted Answer

The midpoint of (a, b) and (c, d) =

Given: Point A is the midpoint between points (5,8) and (-3, -2)
So,  the coordinates of point A  =   = (2/2, 6/2) =  (1, 3)

Given: The midpoint between point A and point B is  (4, -1) 
So, we don't know the coordinates of point B
Let the coordinates of point B = (x, y)

Applying the formula, we get:  1  + x)/2, ( 3  + y)/2] =  (4, -1) 
This means ( 1  + x)/2 =  4 
Solve to get: x = 7

It also means ( 3  + y)/2 =  -1 
Solve to get: y = -5

So, the coordinates of point B = (7, -5)
So, point B is in quadrant IV

https://gmatclub.com/forum/download/file.php?mode=view&id=35654

Answer:  D

pushpitkc · Answer

Midpoint of 2 points (x1,y1) and (x2,y2) can be calculated by using ( \frac{x1+x2}{2} , \frac{y1+y2}{2} )

Now coming to the question at hand.

Given:   Points A(5,8) and B(-3,-2)

The midpoint is (1,3). Let's call this point X

Given:   The midpoint of points Y(a,b) and X(1,3) is (4,-1)

Using midpoint formula, we get  \frac{(a+1)}{2} = 4  and  \frac{(b+3)}{2} = -1

Therefore, we can get point Y(a,b) to be (7,-5) which is in the IV quadrant (Option D)

mws3 · Answer

(7, -5) is obviously in the IV quadrant

TheKingInTheNorth · Answer

OA is D ?

(5,8)---------------Mid point A ( 1,3 ) ------------------ (-3, -2)

To cal the mid point 
(5 +(-3))/2=1 
(8 + (-2))/2=3

Now 
A(1,3)-------------Mid point ( (4, -1) ----------B(x,y) 
we are required to cal. B ( x,y)

By Mid Point Rule

B is ( 7,-5) .

Hence IV quadrant

Nunuboy1994 · Answer

In order to solve this question we need to know the midpoint formula- however, there is an interesting way to look at this formula. Rather than memorize the formula, notice that the x coordinates for the midpoint are simply the average two given x values- so it doesn't matter which order you add them in (commutative property of addition). Also, the y coordinate of the midpoint is just the average of the two y values. This is perhaps a better way to look at the formula so as to have it stick in your head like riding a bike. But anyways, the question stem gives us a midpoint between two coordinates, we don't necessarily have to call these coordinates anything or draw diagram- just take the average of both x coordinates and the average of both y coordinates in order to find the midpoint. We then just reverse engineer and use algebra in order to find the missing variable in our midpoint formula for B- in simple terms, the average of a's x coordinate and the x coordinate of some other point must equal the x coordinate of B AND the average point A's y coordinate and some other point must equal the y coordinate of B.

1 + x /2 = 4 
 1 + x= 8 
 x= = 7

3 + y/2= -1
 3 + y = -2 
 y= -5

kawal27 · Answer

MID POINT FORMULA = (X1+X2)/2 , (Y1+Y2)/2

(5+(-3))/2 =1
(8+(-2))/2=3 
A=1,3
 now midpoint of a and b = (X+1)/2=4
 thus X=3
similarly,(Y+3)/2=-1
 thus Y=-5 
 so B=3,-5

which lies in IV quadrant
ANS:D

nahid78 · Answer

To solve this question we do not need to calculate B. Line (1,3) and (4,-1) gives the hint we need.

Rainman91 · Answer

We can use the mid point formula to find coordinate of A, then we can simply jot down the 2 points and easily see that the point lies on the 4th quadrant.

Rainman91 · Answer

I solved it without using the mid point formula. Not suggesting you should do it, but see if it helps out.

I drew a scrappy coordinate with the points 5,8 and -3,2.

Realized that A should be in quadrant 1.

Since mid point is 4, -1, which is the 4th quadrant, it must further extend towards the bottom right. Thus the answer has to be quadrant 4.

x---------------|---------------*(5,8)
x---------------|
x---------------|
x---------------|
x---------------|-----*A
x---------------|
x---------------|
x---------------|
----------------------------------
x---------------|--------------*(4, -1)
x---------------|
x__*(-3,-2)__|
x---------------|
x---------------|
x---------------|
x---------------|

Even if you weren't able to guess that A was in quad 1, 2 or 3 you can still figure out the generation direction of B. 
(This is more of a visual way of solving it.)

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