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

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In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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06 Jun 2017, 10:32
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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

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In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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06 Jun 2017, 10:46
1
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)
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Re: In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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06 Jun 2017, 10:52
pushpitkc wrote:
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)
Midpoint is (1,3). Lets call this point X

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

So $$\frac{(a+1)}{2} = 4$$ and $$\frac{(b+3)}{2} = -1$$
Hence we can get point (a,b) to be (7,-5) which is obviously in the II quadrant(Option B)

(7, -5) is obviously in the IV quadrant
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Re: In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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06 Jun 2017, 10:59
Top Contributor
Bunuel wrote:
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

The midpoint of (a, b) and (c, d) = [(a+c)/2, (b+d)/2]

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

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Re: In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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10 Jun 2017, 06:56
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) .

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Re: In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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15 Jun 2017, 21:20
Bunuel wrote:
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

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
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Re: In the coordinate geometry plane, point A is the midpoint between poin  [#permalink]

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12 Aug 2018, 03:58
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Re: In the coordinate geometry plane, point A is the midpoint between poin   [#permalink] 12 Aug 2018, 03:58
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