In what ratio is the segment joining the points (-2,-3) and (3,7) divides by the y-axis? Also, find the coordinates of the point of division.
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In what ratio is the segment joining the points (-2,-3) and (3,7) divides by the y-axis? Also, find the coordinates of the point of division.
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Answer:
y is dividing the line so coordinates of this points is (0,y)
by using section formula ,we got the answer and by separating X and y coordinates we got answer
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Answer:
Let the required point be P( 0, y)
Also, let the required ratio be k : 1
Using section formula,
P(0,y) = [(m1*x2+m2*x1) / m1+m2 , (m1*y2 +m2*y1) / m1+ m2]
Substituting values m1=k , m2=1, x1= -2 ,x2= 3 , y1=-3, y2=7, We get
P(0.y) = [ (3*k +1*-2)/ k+1 , (7*k +1*-3) /k+1]
P(0,y) = [ (3k-2)/ k+1 , (7k-3)/ k+1]
0= (3k-2)/k+1...(a) , y= (7k-3)/k+1......(b)
(a) ..3k-2 = 0
3k = 2
k=2/3
Sub k= 2/3 in (b)
y = (7*(2/3) - 3)/ (2/3)+1
=(14/3 - 3)/ 5/3
= (14-9)/3 / (5/3)
= (5/3) /(5/3)
= 1
Therefore ratio is k :1 = 2/3 :1 = 2:3
and point of division is P( 0,1)