Question

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

Answer 1

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

$P(x, y)=[\frac{Mx_2+Nx_1}{M+N}, \frac{My_2+Ny_1}{M+N}]$

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.

$P(m,6)=[\frac{Mx_2+Nx_1}{M+N}, \frac{My_2+Ny_1}{M+N}]$ --- ( i )

On comparing Ordinate of P with LHS we get

$6 =  \frac{My_2+Ny_1}{M+N}$

Putting values of y₁ as Ordinate of A and y₂ s Ordinate of B

$6= \frac{8M+5N}{M+N}$

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