Coordinate Geometry Question 25
Question: The points $ ( \frac{a}{\sqrt{3}},a ),\ ( \frac{2a}{\sqrt{3}},2a ),\ ( \frac{a}{\sqrt{3}},3a ) $ are the vertices of
Options:
A) An equilateral triangle
B) An isosceles triangle
C) A right angled triangle
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ A( \frac{a}{\sqrt{3}},a ),B( \frac{2a}{\sqrt{3}},2a ) $ and $ C( \frac{a}{\sqrt{3}},3a ) $ Then $ AB^{2}={{( \frac{a}{\sqrt{3}}-\frac{2a}{\sqrt{3}} )}^{2}}+{{(a-2a)}^{2}}=\frac{a^{2}}{3}+a^{2}=\frac{4a^{2}}{3} $ Similarly $ BC^{2}=\frac{4a^{2}}{3} $ and $ AC^{2}=4a^{2} $
Hence it is an isosceles triangle.
BETA
