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Q)

Find the ratio in which x axis divides the line joining (5,6)and(-1,-4)

Find the ratio in which x axis divides the line joining (5,6)and(-1,-4)

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A)

Let the point on X-axis be P(x,0) since the y-coordinate is always zero on X-axis.
Given A(2, 3) and B(5, 6)
Let P divides the line segment joining the points (5, 6) and (-1, -4) in the ratio m:1

Coordinates of P=(mx2+x1/(m+1),my2+y1/m+1)

(x,0)=((-m+5)/m+1  ,-4m+6/m+1)

Comparing both sides

-4m+6/m+1=0

-4m+6=0

-4m=-6

M=6/4

M=3/2

M:1=3/2:1

=3:2

Therefore, P divides the line segment joining two points in the ratio 3 : 2 externally.

 

 

 

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