Three-Dimensional-Geometry Question 427
Question: The triangle formed by the points (0, 7, 10), (?1, 6, 6), (? 4, 9, 6) is
[RPET 2001]
Options:
A) Equilateral
B) Isosceles
C) Right angled
D) Right angled Isosceles
Show Answer
Answer:
Correct Answer: D
Solution:
Let A be (0, 7, 10), B (?1, 6, 6) and C (? 4, 9, 6) Then, $ AB=\sqrt{1+1+16}=\sqrt{18}=3\sqrt{2} $ $ BC=\sqrt{9+9+0}=\sqrt{18}=3\sqrt{2} $ $ AC=\sqrt{16+4+16}=\sqrt{36}=6 $ Clearly, $ AC^{2}=AB^{2}+BC^{2} $ Hence $ \Delta $ is right angled. Also, since $ AB=BC $ \ $ \Delta $ is right angled isosceles.
BETA
