Which of the following sets of co-ordinates does not represent the vertices of an isosceles triangle.
Coordinate Geometry (Courtesy: learningwave.com)
A) (0,2), (0,-2), (2,0)
B) (1,3), (1,5), (3,4)
C) (1,3), (1,7), (4,5)
D) (2,2), (2,0), (1,1)
E) (2,3), (2,5), (3,3)
the answer is D)option
e
yap its E).
Yes, it is definitely E
anyone with appeoach pls ??
answer is E
E)
Dear Neeths and Archana,
I wanna know your approach ??
the first option is ruled out by observation.
in options b,c,d:two points have their x-coordinates same but y-coordinates different.the remaining third point has the y-coordinate in middle of the y-coordinates of the other two points.
for eg,consider option c:A(1,3),B(1,7),C(4,5)
pts A and B have their x-coordinates equal.
y-coordinate of C is in middle of the y-coordinates od A and B.
so,it will form an isoceles triangle.
Hi dhaval,
Thanks for your logical approach, but there are some more approach also.
Correct answer is E.
is the other approach is by using distance formula ?
yes of course ! can you write it for others ?
ans is E
i merely used the distance formula..
distance between 2 points (x1,y1) and (x2,y2) is
((x2-x1)^2 + (y2-y1)^2)^1/2
Thanks neeths for sharing us.
E
Yes the ans is E but then it can be merely found out by observation….as it will save time…..by drawing figure….making a rough sketch….i found this methon more appealing….
gr8 neeths
im not gettin the ans using distance formula….did any1 else get it?
yeah its very simple ..,,mark the points roughly in the graph and u will very easily see that one of the give points is equidistant from the other two ,in each of the sets that is…..
E
answer is E)
in all the options except last one of the coordinates of the first two points are same and the mean of the other coordinate of the first two points is equal to that coordiante of the third point….which proves that tey are isosceles triangle
e
the distance formula takes time…observation is much simpler for such a problem..just locate the points on a graph..