The points , and are vertices of
- A.an obtuse angled triangle
- B.an acute angled triangle
- C.a right angled triangle
- D.None of the above
Show answer and solution
Correct option: D
Solution
Check if the three points are collinear.
Slope from (0, 8/3) to (1, 3): (3 - 8/3)/(1 - 0) = (1/3)/1 = 1/3.
Slope from (1, 3) to (82, 30): (30 - 3)/(82 - 1) = 27/81 = 1/3.
Both slopes are equal, so all three points are collinear — they lie on the same straight line. Therefore they do not form any triangle at all, and the answer is "None of the above."
Slope from (0, 8/3) to (1, 3): (3 - 8/3)/(1 - 0) = (1/3)/1 = 1/3.
Slope from (1, 3) to (82, 30): (30 - 3)/(82 - 1) = 27/81 = 1/3.
Both slopes are equal, so all three points are collinear — they lie on the same straight line. Therefore they do not form any triangle at all, and the answer is "None of the above."
[1986]