Coordinate Geometry Question 38
Question: The points $ (0,0),\ (a,0) $ and $ ( \frac{a}{2},\frac{a\sqrt{3}}{2} ) $ are vertices of
Options:
A) Isosceles triangle
B) Equilateral triangle
C) Scalene triangle
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ A(0,0),B(a,0) $ and $ C( \frac{a}{2},\frac{a\sqrt{3}}{2} ) $
Hence $ AB=\sqrt{a^{2}+0}=a,BC=\sqrt{{{( \frac{a}{2} )}^{2}}+{{( \frac{a\sqrt{3}}{2} )}^{2}}}=a $ and $ AC=\sqrt{{{( \frac{a}{2} )}^{2}}+{{( \frac{a\sqrt{3}}{2} )}^{2}}}=a $
Hence the triangle is equilateral.
BETA
