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23 May 2018, 22:53
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
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63% (01:22) correct
37%
(01:29)
wrong
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In the coordinate plane, a triangle has points (4,6), (8,6), and (x,y). Is this triangle isosceles?
(1) x = 6
(2) y = 9
(1) x = 6
(2) y = 9
24 May 2018, 00:47
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Solution
Given:
• In a given triangle in the coordinate plane, the vertices are (4, 6), (8, 6), and (x, y)
To find:
• Whether the mentioned triangle is isosceles or not
Analysing Statement 1
• As per the information provided in Statement 1, x = 6
- o As we already know that the points are forming a triangle, y cannot be equal 6. Otherwise the points will not be able to form a triangle
• The line x = 6 is the perpendicular bisector of the line joining the points (4, 6) and (8, 6)
Also, any points on the perpendicular bisector, which are in the form (6, y), will always be equidistant from the points (4, 6) and (8, 6)
- • Hence, it will definitely form an isosceles triangle
Therefore, statement 1 is sufficient to answer
Analysing Statement 2
• As per the information provided in Statement 2, y = 9
• Given the y-coordinate of the 3rd point is fixed, the x coordinate can vary and depending on the values of x, we can have multiple possibilities as shown in the diagram below:
- • Keeping y = 9, if the value of x is 6 then it forms an isosceles triangle
• But, if x = 5 or x = 8, the triangles formed are not isosceles triangle
Hence, statement 2 is not sufficient to answer the question
Hence, the correct answer is option A.
Answer: A
General Discussion
24 May 2018, 00:37
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Answer will be C
with distance formula of (4,6) & (8,6)= 2
1.x=6, we cant calculate distance as y is needed
2. y=9, we cant calculate distance as x is needed
merging both statements, we get distance between (4,6) & (6,9)= root 13
same for (8,6) & (6,9)= root 13, Hence, answer is C
with distance formula of (4,6) & (8,6)= 2
1.x=6, we cant calculate distance as y is needed
2. y=9, we cant calculate distance as x is needed
merging both statements, we get distance between (4,6) & (6,9)= root 13
same for (8,6) & (6,9)= root 13, Hence, answer is C
