The line regiment joining the point in (5,7) and N(-3, 2)
is interreted by the y axis at point l write down
the abscesra of l Hance find the ratio in which
it divides MN Also find the co-ordinates of
yasis at point to write down
Answers
Step-by-step explanation:
Given :-
The line segment joining the points M (5,7) and N(-3, 2) is intersectedby the y axis.
To find :-
Find the ratio in which it divides MN Also find the co-ordinates of y-axis ?
Solution :-
Given points are M(5,7) and N(-3,2)
If they are intersecting at a point on y-axis
Let the point be (0,y)
Let the required ratio = m:n
Let (x1, y1) = (5,7)=> x1 = 5 and y1 = 7
Let (x2, y2) = (-3,2)=> x2 = -3 and y2 = 2
We know that
The coordinates of a point P(x,y) which divides the linesegment joining the points (x1, y1) and (x2, y2) is
({mx2+nx1}/(m+n) ,{my2+ny1}/(m+n) )
On Substituting these values in the above formula
=>({(m)(-3)+(n)(5)}/(m+n),{(m)(2)+n(7)}/(m+n))
=>( { -3m+5n} /(m+n) , { 2m+7n}/(m+n)
According to the given problem
Intersecting point is (0,y)
=> ( { -3m+5n} /(m+n) , { 2m+7n}/(m+n) = (0,y)
On Comparing both sides then
=> (-3m+5n} /(m+n) = 0 and
{2m+7n}/(m+n) = y-----------(1)
=> (-3m+5n) = 0(m+n)
=> -3m +5n = 0
=> -3m = -5n
=> 3m = 5n
=> 3m/n = 5
=> m/n = 5/3
=> m :n = 5:3
=> m = 5 and n = 3
On Substituting the values of m and n in (1) then
=>{2m+7n}/(m+n) = y
=> [(2)(5)+7(3)]/(5+3) = y
=>y = (10+21)/8
=> y = 31/8
The point = (0,31/8)
Answer:-
The required ratio which divides the linesegment MN is 5:8
The required point of y -axis is (0,31/8)
Used formulae:-
The coordinates of a point P(x,y) which divides the linesegment joining the points (x1, y1) and (x2, y2) is
({mx2+nx1}/(m+n) ,{my2+ny1}/(m+n) )
- The equation of y-axis is x=0