Coordinate Geometry Question 172
Question: ABC is an isosceles triangle. If the coordinates of the base are B (1,3) and C (- 2, 7), the coordinates of vertex A can be
[Orrissa JEE 2002; Pb. CET 2002]
Options:
A) (1, 6)
B) $ ( -\frac{1}{2},5 ) $
C) $ ( \frac{5}{6},6 ) $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The vertex $ A(x,y) $ is equidistant from B and C because ABC is an isosceles triangle. Therefore, $ {{(x-1)}^{2}}+{{(y-3)}^{2}}={{(x+2)}^{2}}+{{(y-7)}^{2}} $
$ \Rightarrow 6x-8y+43=0 $ Thus, any point lying on this line can be the vertex A except the mid-point $ ( -\frac{1}{2},5 ) $ of BC.
BETA
