Find the ratio in which the points p(m,6) divides the line segment joining the points A(-4,5) and B(2,8). Also find the value of m
Answers
Answer:
1 : 2, m = -3
Step-by-step explanation:
Here End Points of Line Segment are A(-4, 5) and B(2, 8)
Coordinates of point, which divides AB, are (m, 6)
Let the ratio in which P divides AB is M:N
We know, to find coordinates of point of division we use section formula
Where P(x, y ) are coordinates of that point which divides a line segment, (x₁, y₁) and (x₂, y₂) are coordinates of end points of the line segment. M and N is the ratio in which the line segment is divided.
--- ( i )
On comparing Ordinate of P with LHS we get
Putting values of y₁ as Ordinate of A and y₂ s Ordinate of B
6M + 6N = 8M + 5N
2M = N
M/N = 1/2
∴ Ratio is 1 : 2
Now, from eq( i ) we can see
m = (Mx₂ + Nx₁)/(M+N)
Putting value of x₁ from coordinates of A and x₂ from coordinates of B
m = (2×1 +2×(-4))/(1+2) [∵ M - 1 and N = 2]
m = (2 - 8)/3
m = -3