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In the coordinate geometry plane, point A is the midpoint between poin
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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
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06 Jun 2017, 10:46
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
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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
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06 Jun 2017, 10:59
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 = 4Solve to get: x = 7 It also means ( 3 + y)/2 = 1Solve to get: y = 5 So, the coordinates of point B = (7, 5) So, point B is in quadrant IV Answer:
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Re: In the coordinate geometry plane, point A is the midpoint between poin
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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) . Hence IV quadrant
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Re: In the coordinate geometry plane, point A is the midpoint between poin
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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
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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
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