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In the coordinate geometry plane, point A is the midpoint between poin
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22 Mar 2021, 10:28
22 Mar 2021, 10:28
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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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. I
B. II
C. III
D. IV
E. None of the above
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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Re: In the coordinate geometry plane, point A is the midpoint between poin
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22 Mar 2021, 10:55
22 Mar 2021, 10:55
1
Carcass 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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. I
B. II
C. III
D. IV
E. None of the above
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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
Answer: D
Re: In the coordinate geometry plane, point A is the midpoint between poin
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24 Mar 2021, 02:22
24 Mar 2021, 02:22
1
The only idea that one should know for this question is the midpoint calculation
Point A= midpoint of given points (5,8) & (-3,-2)
Point A= ((5+(-3))/2,(8+(-2))/2) = (1,3)
The midpoint of Point A and Point B is given as (4,-1)
assuming Point B to be (a,b)-
(1+a)/2 =4 and (1+b)/2 =-1
a=7 and b=-3, hence point B =(7,-3) which lies in the 4th quadrant
Option D is correct
Point A= midpoint of given points (5,8) & (-3,-2)
Point A= ((5+(-3))/2,(8+(-2))/2) = (1,3)
The midpoint of Point A and Point B is given as (4,-1)
assuming Point B to be (a,b)-
(1+a)/2 =4 and (1+b)/2 =-1
a=7 and b=-3, hence point B =(7,-3) which lies in the 4th quadrant
Option D is correct
