Question

Find the ratio in which the line segment joining the points (6, 4) and (1, -7) is divided by the x-axis

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Given:-

The points (6, 4) and (1, -7)

To find:-

Find the ratio in which the line segment joining the points (6, 4) and (1, -7) is divided by the x-axis.

Solution:-

Given points are (6, 4) and (1, -7)

(x1, y1)=(6,4)=>x1 = 6 and y1 = 4

(x2, y2)=(1,-7)=>x2 = 1 and y2 = -7

Let the required ratio is m1:m2

The point which divides the given points is (x,0)

Since it is given that x - axis

We know that the section formula

[(m1x2+m2x1)/(m1+m2) , (m1x2+m2x1)/(m1+m2)]

On Substituting the values in the above formula

=>[{m1(1)+m2(6)}/(m1+m2) , {m1(-7)+m2(1)}/(m1+m2)]

=(0,x)

=>[(m1+6m2)/(m1+m2),(-7m1+m2)/(m1+m2)] = (0,x)

On comparing both sides then

=>(m1+6m2)/(m1+m2) = 0

=>m1+6m2 = 0(m1+m2)

=>m1+6m2 = 0

=>m1 = -6m2

=>m1/m2 = -6

=>m1/m2 = -6/1

Therefore, m1:m2 = -6:1

Answer:-

The ratio in which the line segment joining the points (6, 4) and (1, -7) is divided by the x-axis is -6 : 1

Used formula:-

• The equation of x-axis is y=0

The section formula:-

The point which divides The linesegment joining the two points (x1, y1) and (x2, y2) in the ratio m1:m2 is

[(m1x2+m2x1)/(m1+m2) , (m1x2+m2x1)/(m1+m2)]