Question

(-6,a) divides the join of A(-3,1) and B(-8,9) also find the value of A.

Answer 1

Question:

Find the ratio in which the point P(-6,a) internally divides the line joining the points A(-3,1) and B(-8,9). Also, find the value of a.

Answer:

The point P(-6,a) internally divides the line joining the points A(-3,1) and B(-8,9) in the ratio 3:2 .

Also , a = 29/5 .

Note:

Section formula:

• If a point P(x,y) internally divides the line joining the points A(x1,y1) and B(x2,y2) , then the coordinates of the point P is given by;

x = (m•x2 + n•x1)/(m + n)

y = (m•y2 + n•y1)/(m + n)

• If a point P(x,y) externally divides the line joining the points A(x1,y1) and B(x2,y2) , then the coordinates of the point P is given by;

x = (m•x2 - n•x1)/(m - n)

y = (m•y2 - n•y1)/(m - n)

Solution:

Let the point P(-6,a) internally divides the line joining the points A(-3,1) and B(-8,9) in the ratio

m:n .

Thus,

As per the section formula, the x-coordinate of the point P will be given as;

=> -6 = {m•(-8) + n•(-3)}/(m + n)

=> -6 = (-8m - 3n)/(m + n)

=> -6 = -(8m + 3n)/(m + n)

=> 6 = (8m + 3n)/(m + n)

=> 6•(m + n) = 8m + 3n

=> 6m + 6n = 8m + 3n

=> 8m - 6n = 6n - 3n

=> 2m = 3n

=> m/n = 3/2

=> m:n = 3:2

Hence,

The point P(-6,a) internally divides the line joining the points A(-3,1) and B(-8,9) in the ratio 3:2 .

Also,

As per the section formula, the y-coordinate of the point P will be given as;

=> a = (m•9 + n•1)/(m + n)

=> a = (3•9 + 2•1)/(3 + 2)

=> a = (27 + 2)/5

=> a = 29/5

Hence,

Required value of a is 29/5.