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

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

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

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

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

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

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.

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.)