Find the ratio in which the y-axis divides the line segment joining the points
(5, -6) and (-1. -4). Also find the coordinates of the point of intersection.
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Find the ratio in which the y-axis divides the line segment joining the points
(5, -6) and (-1. -4). Also find the coordinates of the point of intersection.
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To find:
Formula required:
[ where (x,y) are the coordinates of point which divide line segment joining points (x₁, y₁) and (x₂, y₂) in the ratio m : n ]
Solution:
[ x coordinate would be zero because point of division lies in y-axis ]
Now,
Using Section Formula
so,
Taking
Now, taking
putting value of k
Hence,
Verified answer
Answer:
Ratio is...1:5 and
co-ordinate is..(0,-25/6).
Let us consider the ratio as k:1.
As the line passes through the y-axis
so the coordinates at y-axis will be (0,y).....(i)
now by using formula.... x=(mx1 + nx2)/(m+n)
thereby using equation (i)
0=(5k+(-1))/1+k
0=5k-1
1=5k
1/5=k...
ratio is K:1
i.e. 1:5
now putting this in y ordinate
y=((5×1)+(-6)×5)/(1+5)
y=(5-30)/6
coordinates is (0,-25/6)
y= -25/6