# Image of a Point with respect to a line [Short Trick] – 7tricks

So, today we gonna tell you the secret trick to find the image of a point with respect to a line in 15 seconds, literally it will not take more than 15 seconds. Whatever the question is for a 2D plane or a 3D plane, the trick works for both.

First, We welcome you to 7tricks, it is a platform of amazing short tricks and mnemonics. Now before going on the trick we learn about the method and approach for finding image of a point in a plane.

#### How to find the image of a point

Basically, In simple ways, if the question says to find the image of a point along a line, then we know that

• The image distance from that line and the point will be the same. So, for solving let the image point be (h,k) then find distance with the given line, after that find distance between the given line and given point and put the multiplication of solve -1 (m1.m2 = -1).
• In the second step, find the slope of the line(if the line equation is ax+by+c=0 then the slope will be -a/b) now find the slope of the line joining the given point and image point by the formula (y2-y1)/(x2-x1).
• Formula derived by this will be-
xx1a=yy1b=(ax1+by1+c)a2+b2

#### Trick to find the image of a point

Now move toward the trick, follow these steps:-

Let you have a point (y,z) and find the image of this point along line ax+by+c= 0. Suppose the answer will be (h,k). Now, write h-y/a = k-z/b = -2(ay + bz + c)/a^2 + b^2.

Let’s try out with some examples:-

QuestionFind the image of the point (3,8) with respect to the
line x+3y = 7 assuming the line to be a plane mirror.

Solution: Let points are (h,k). So,
h-3/1 = k-8/3 = -2[3 + 3(8) – 7]/1 + 9
By, solving these two equations we got
h = -1 and k = -4

It took less than 15 seconds.
This trick can help you in finding the image of a
point very fast to save your time in exams.
Note:- This trick works for the 3D planes also.

Hope you liked this trick!

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