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15 Jan 2021, 03:15
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In the standard (x,y) coordinate plane, a straight line segment is drawn to connect (0,0) and (4,4). Which of the following sets of points, when connected by a straight line segment, will intersect the original segment?
(A) (–3,3) and (3,4)
(B) (0,–1) and (4,3)
(C) (0,1) and (4,5)
(D) (1,0) and (8,4)
(E) (2,1) and (2,5)
(A) (–3,3) and (3,4)
(B) (0,–1) and (4,3)
(C) (0,1) and (4,5)
(D) (1,0) and (8,4)
(E) (2,1) and (2,5)
15 Jan 2021, 03:39
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The first line segment has slope of 1.So any line segment that intersects it cannot have a slope of 1. So lines B and C are ruled out.
Among remaining 3 options, A has slope - 1/6,D has slope 4/7 and E has infinite slope, i.e. parallel to the y axis.
For point E, since we know that x value will remain constant at 2, we see that it will cross the point (2,2) so it will intersect the first line.
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Among remaining 3 options, A has slope - 1/6,D has slope 4/7 and E has infinite slope, i.e. parallel to the y axis.
For point E, since we know that x value will remain constant at 2, we see that it will cross the point (2,2) so it will intersect the first line.
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As far as my rational goes, due to the diction "will intersect the original segment", only Option E gets us the correct value of (2,1), where the line segment meets the original, however its slope is undefined (parallel to Y-Axis).
Option A & D implies that those line segments will have positive slopes but they don't cut across the original segment.
And solving Option B & C fetches us slope of 1 identical to original line segment.
So Its option E.
Please correct my reasoning if got wrong.
Regards
Shubham
Option A & D implies that those line segments will have positive slopes but they don't cut across the original segment.
And solving Option B & C fetches us slope of 1 identical to original line segment.
So Its option E.
Please correct my reasoning if got wrong.
Regards
Shubham
