If an invigilator at the point I, lying on the straight line Joining B and C such that it divides the distancebetween them in the ratio of 1 :2. Then coordinates of I are *
1 point
(6,1)
(9,1)
Option 3
Option 4
Answers
Answer:
Using the section formula, if a point (x,y) divides the line joining the points (x
1
,y
1
) and (x
2
,y
2
) in the ratio m:n, then
(x,y)=(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
3AC=CB
CB
AC
=
3
1
Since, A(1,1) and B(2,3) & m:n=1:3
Therefore, we have
C(
m+n
mx
2
+nx
1
,
m+n
my
2
+ny
1
)
(
1+3
(1)(2)+3(1)
,
1+3
(1)(3)+3(1)
)
C→(
4
5
,
2
3
).
Given: An invigilator at point l lying on a straight line divides B(6,1) and C(9,1) in the ratio 1:2
To find: The coordinates of l
Explanation: For internal division of a straight line in a particular ratio, the formula used is:
( mx2+nx1/m+n, my2+ny1/m+n)
Here, l divides B(6,1) and C(9,1) in the ratio 1:2
Therefore, m=1, n=2 , x1=6, x2= 9 , y1=y2 = 1
l= ( 1*9+2*6/ 1+2, 1*1+2*1/1+2)
= (21/3, 3/3)
= (7,1)
Checking, distance of 6,1 from 7,1 = 7-6 = 1 units
Distance of 9,1 from 7,1= 9-7 = 2 units
It proves 7,1 divides 6,1 and 9,1 in 1:2.
Therefore, the coordinates of l are (7,1).