Determine the ratio in which the point (-6, a) divides the join of A(-3, 1) and B(-8, 9). Also find the value of a.
Answers
Given : The point (-6, a) divides the join of A(-3, 1) and B(-8, 9).
Solution :
Let the point (-6, a) divides the join of A(-3, 1) and B(-8, 9) in the ratio be m1 : m2 .
By using section formula :
P(x,y) = [ (m1x2 + m2x1)/m1 + m2 , (m1y2 + m2y1)/m1 + m2]
For point P (-6,a) :
-6 = (m1 × - 8 + m2 × -3)/ m1 + m2
(- 6)(m1 + m2) = - 8m1 - 3m2
-6m1 - 6m2 = - 8m1 - 3m2
-(6m1 + 6m2) = - (8m1 + 3m2)
6m1 + 6m2 = 8m1 + 3m2
6m1 - 8m1 = 3m2 - 6m2
-2m1 = - 3m2
2m1 = 3m2
m1/m2 = 3/2
m : n = 3 : 2
Hence the ratio in which the point (-6, a) divides the join of A(-3, 1) and B(-8, 9) is 3 : 2
Now,
a = (m1 × 9 + m2 × 1)/(m1 + m2)
a = (3 × 9 + 2 × 1)/ (3 + 2)
a = (27 + 2)/5
a = 29/5
Hence the value of a is 29/5.
HOPE THIS ANSWER WILL HELP YOU……
Some more questions :
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 division.
https://brainly.in/question/15938453
Find the co-ordinates of a points on x-axis which is equidistant from the points (–2,5) and (2,�3)
brainly.in/question/3057505
Step-by-step explanation:
a=29/5I hope is helpful for you