Q. 9

# Show that the length of the perpendicular from the point (7, 0) to the line 5x + 12y – 9 = 0 is double the length of perpendicular to it from the point (2, 1)

Answer :

Given: Points (7,0) and (2,1) , line 5x + 12y – 9 = 0

To Prove : length of the perpendicular from the point (7, 0) to the line 5x + 12y – 9 = 0 is double the length of perpendicular to it from the point (2, 1)

Formula used:

We know that the length of the perpendicular from (m,n) to the line ax + by + c = 0 is given by,

D

Let D_{1} be the length of perpendicular from the point (7, 0) to the line 5x + 12y – 9 = 0

The given equation of the line is 5x + 12y – 9 = 0

Here at point (7,0) m= 7 and n= 0 , a = 5 , b = 12 , c = -9

D_{1}

D_{1}

D_{1}

Let D_{2} be the length of perpendicular from the point (2, 1) to the line 5x + 12y – 9 = 0

The given equation of the line is 5x + 12y – 9 = 0

Here at point (2,1) m= 2 and n= 1 , a = 5 , b = 12 , c = -9

D_{2}

D_{2}

D_{2}

D_{1}=2D_{2}=2

Thus the length of the perpendicular from the point (7, 0) to the line 5x + 12y – 9 = 0 is double the length of perpendicular to it from the point (2, 1)

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