wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

If the algebraic sum of the perpendicular distances from the points (2,0),(0,2) and (1,1) to a variable straight line be zero, then the line passes through the point

A
(1,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(1,1)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
(1,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(1,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C (1,1)
Let the variable line be ax+by+c=0
Given, the algebraic sum of the perpendicular from the points (2,0),(0,2) and (1,1) to this line is zero
2×a+b×0+ca2+b2+a×0+b×2+ca2+b2+a×1+b×1+ca2+b2=0
±(2a+ca2+b2)±(2b+ca2+b2)±(a+b+ca2+b2)=0
2a+c+2b+c+a+b+c=0
3a+3b+3c=0
a+b+c=0
This is a linear relation between a,b and c.
So, the equation ax+by+c=0 represents a family of straight line passing through a fixed point.
Comparing ax+by+c=0 and a+b+c=0
We obtain
The coordinates of fixed point are (1,1).

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Definition and Standard Forms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon