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20 Jun 2015, 10:11
Kudos
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In the xy-plane, line \(m\) has a y-intercept of -2. If line \(m\) passes through the midpoint of the line segment with endpoints (2, 4) and (6, -8), what is the slope of line \(m\)?
A. \(-3\)
B. \(-1\)
C. \(-\frac{1}{3}\)
D. \(0\)
E. \(Undefined\)
A. \(-3\)
B. \(-1\)
C. \(-\frac{1}{3}\)
D. \(0\)
E. \(Undefined\)
20 Jun 2015, 10:11
Kudos
Bookmarks
Official Solution:
In the xy-plane, line \(m\) has a y-intercept of -2. If line \(m\) passes through the midpoint of the line segment with endpoints (2, 4) and (6, -8), what is the slope of line \(m\)?
A. \(-3\)
B. \(-1\)
C. \(-\frac{1}{3}\)
D. \(0\)
E. \(Undefined\)
The y-intercept of line \(m\) being -2 indicates that \(m\) passes through the point (0, -2).
The coordinates of the midpoint of the line segment with endpoints (2, 4) and (6, -8) are calculated as \((\frac{2+6}{2}, \frac{4 + (-8)}{2})\) which gives (4, -2).
So, we need to determine the slope of the line that goes through the points (0, -2) and (4, -2). Since the line through these points is horizontal, its slope is 0.
Note that while Geometry is not tested on GMAT Focus, Coordinate Geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
Answer: D
In the xy-plane, line \(m\) has a y-intercept of -2. If line \(m\) passes through the midpoint of the line segment with endpoints (2, 4) and (6, -8), what is the slope of line \(m\)?
A. \(-3\)
B. \(-1\)
C. \(-\frac{1}{3}\)
D. \(0\)
E. \(Undefined\)
The y-intercept of line \(m\) being -2 indicates that \(m\) passes through the point (0, -2).
The coordinates of the midpoint of the line segment with endpoints (2, 4) and (6, -8) are calculated as \((\frac{2+6}{2}, \frac{4 + (-8)}{2})\) which gives (4, -2).
So, we need to determine the slope of the line that goes through the points (0, -2) and (4, -2). Since the line through these points is horizontal, its slope is 0.
Note that while Geometry is not tested on GMAT Focus, Coordinate Geometry is tested under the Functions and Graphing sections found in the Official Guide for GMAT Focus Edition.
Answer: D
27 Sep 2019, 00:58
Kudos
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I solved it with a different approach.
1) The y-intercept of line mm is -2 means that mm passes through the point (0, -2).
2) The coordinates of the midpoint of the line segment whose endpoints are (2, 4) and (6, -8) is [(2+6)/2 ; 4+(−8)/2]= (4; −2).
Now as per formula,
the slope of a line passing through the points (x1, y1) and (x2, y2) = (y2 -y1) / (X2 - X1)
line m has 2 points as (0, -2) and (4, -2).
Hence Slope of m = ( -2 - (-2) ) / (4 - 0) = 0
1) The y-intercept of line mm is -2 means that mm passes through the point (0, -2).
2) The coordinates of the midpoint of the line segment whose endpoints are (2, 4) and (6, -8) is [(2+6)/2 ; 4+(−8)/2]= (4; −2).
Now as per formula,
the slope of a line passing through the points (x1, y1) and (x2, y2) = (y2 -y1) / (X2 - X1)
line m has 2 points as (0, -2) and (4, -2).
Hence Slope of m = ( -2 - (-2) ) / (4 - 0) = 0
