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Question

The coordinates of the foot of the perpendicular from (a,0) on the line y=mx+am are


A

0,am

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B

0,-am

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C

am,0

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D

-am,0

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Solution

The correct option is A

0,am


Explanation for correct option:

Given that y=mx+am(i)

Step 1:Visualizing the given information.

Slope of the line y=mx+amis 'm'.

So, the slope of AB will be =-1m

Now, AB passes through the points (a,0).

Therefore the equation of AB will be

y-y1=slopex-x1y-0=-1mx-amy=-x+amy+x=a(ii)

Step 2:Finding the coordinates:

Solving equations (i) and (ii)

m2x+a+x-a=0xm2+1=0x=0

Substituting the value of x in equation i

y=m×0+am=am

The point B is 0,am

Hence, option (A) is the correct answer


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