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Question

Image of the point -1,3 w.r.t. the line y=2x is


A

-1,-5

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B

1,3

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C

3,1

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D

5,1

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Solution

The correct option is C

3,1


Explanation for the correct option.

Find the coordinates of the image.

If the image of the point x1,y1 with respect to line ax+by+c=0 is h,k then:

h-x1a=k-y1b=-2ax1+by1+ca2+b2

Here the line is y=2x and it can be written as: -2x+y=0.

So a=-2,b=1,c=0.

The point is -1,3. So x1=-1,y1=3.

Thus the coordinates of the image h,k is given by substituting all the values in the formula

h--1-2=k-31=-2(-2)×-1+1×3+022+-12⇒h+1-2=k-31=-22+34+1⇒h+1-2=k-31=-2×55⇒h+1-2=k-31=-2

First solving for h.

h+1-2=-2⇒h+1=4⇒h=3

Now, solving for k.

k-31=-2⇒k-3=-2⇒k=1

So, the coordinates of the image is 3,1.

Thus, the image of the point -1,3 w.r.t. the line y=2x is 3,1.

Hence, the correct option is C.


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