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06 Apr 2023, 01:30
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
68% (02:34) correct
33%
(02:24)
wrong
based on 80
sessions
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Not Attempted Yet
The line y = 2 contains points J, K, L, and M, though not necessarily in that order. The coordinates of J are (3, 2), and the distance between J and K is 12. If the coordinates of L are (−3,2), and the distance between L and M is 10, what is the distance between K and M ?
(1) The x coordinate of M is less than the x coordinate of J.
(2) L is the midpoint between J and K.
(1) The x coordinate of M is less than the x coordinate of J.
(2) L is the midpoint between J and K.
06 Apr 2023, 22:57
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Bunuel
As all the information is w.r.t to the line y = 2, we can plot the information on a number line as shown below. Note, for each point for which the distances are given, we can have the point either on the left of the reference point or on its right.
For example - We know that the distance between J and K is 12. K can be 12 units on the right of J, i.e. the coordinate of K = (15,2) or the point K can be 12 units to the left of K, i.e. the coordinates of K = (-9,2).
Attachment:
1.jpg [ 12.57 KiB | Viewed 1346 times ]
Statement 1
(1) The x coordinate of M is less than the x coordinate of J.
From statement 1, we can identify the coordinate of M = (-13,2)
We don't have any information on the coordinate of K, hence the statement alone is not sufficient to answer the question.
Attachment:
2.jpg [ 13.9 KiB | Viewed 1305 times ]
Statement 2
(2) L is the midpoint between J and K.
From statement 2, we can identify the coordinate of K = (-9,2)
We don't have any information on the coordinate of M, hence the statement alone is not sufficient to answer the question.
Attachment:
3.jpg [ 13.42 KiB | Viewed 1304 times ]
Combined
The statements combined help us to get two unique points on the plane. Hence the statements combined are sufficient to answer the question.
Attachment:
4.jpg [ 14.71 KiB | Viewed 1269 times ]
Option C
