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21 Sep 2021, 02:26
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In the rectangular coordinate plane, if line segment AB has a length of 10, what are the coordinates of the midpoint of line segment AB?
(1) The slope of line segment AB is -3
(2) The coordinates of point A are (2,6)
(1) The slope of line segment AB is -3
(2) The coordinates of point A are (2,6)
21 Sep 2021, 02:26
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Official Solution:
In the rectangular coordinate plane, if line segment AB has a length of 10, what are the coordinates of the midpoint of line segment AB?
(1) The slope of line segment AB is -3. We know only the slope and the length of AB but not the coordinates of the points. Not sufficient.
(2) The coordinates of point A are (2,6). We know nothing about point B. Not sufficient.
(1)+(2) What do we know? The length of AB, the slope of AB and the coordinates of A. To get the coordinates of the midpoint, we need also to know the exact position of point B. But B can be above point A as well as below point A, so two different positions of B are possible, giving two different coordinates of the midpoint of AB. Not sufficient.
For better understanding check the image below:
Answer: E
In the rectangular coordinate plane, if line segment AB has a length of 10, what are the coordinates of the midpoint of line segment AB?
(1) The slope of line segment AB is -3. We know only the slope and the length of AB but not the coordinates of the points. Not sufficient.
(2) The coordinates of point A are (2,6). We know nothing about point B. Not sufficient.
(1)+(2) What do we know? The length of AB, the slope of AB and the coordinates of A. To get the coordinates of the midpoint, we need also to know the exact position of point B. But B can be above point A as well as below point A, so two different positions of B are possible, giving two different coordinates of the midpoint of AB. Not sufficient.
For better understanding check the image below:
Answer: E
22 Jun 2024, 04:30
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