Coordinate Geometry Question 29
Question: The points $ (-a,-b),\ (a,b),\ (a^{2},ab) $ are
Options:
A) Vertices of an equilateral triangle
B) Vertices of a right angled triangle
C) Vertices of an isosceles triangle
D) Collinear
Show Answer
Answer:
Correct Answer: D
Solution:
$ l_1=\sqrt{{{(2a)}^{2}}+{{(2b)}^{2}}}=2\sqrt{a^{2}+b^{2}} $
$ l_2=\sqrt{{{(a^{2}-a)}^{2}}+b^{2}{{(a-1)}^{2}}}=(a-1)\sqrt{a^{2}-b^{2}} $
$ l_3=\sqrt{{{(a^{2}+a)}^{2}}+b^{2}{{(a+1)}^{2}}}=(a+1)\sqrt{a^{2}+b^{2}} $ Now $ l_1+l_2=l_3. $
Hence points are collinear.
BETA
