Question

the reflection of the point P(1,-2) in the line y=-1

Answer 1

SOLUTION

TO DETERMINE

The reflection of the point P(1,-2) in the line y = - 1

EVALUATION

Here the given point is P(1,-2)

Let P' be the reflection of the point P(1,-2)

The given line is y = - 1

Thus the line y = - 1 bisects the line joining P and P'

Which leads to the midpoint of the line PP' lies on the line y = - 1

Without any loss of generality we assume that the coordinates of P' is (1,k)

Midpoint of the line PP'

$\displaystyle \sf{ = \bigg( \: \frac{1 + 1}{2} , \frac{ - 2 + k}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \: \frac{2}{2} , \frac{ k- 2}{2} \bigg)}$

$\displaystyle \sf{ = \bigg( \: 1 , \frac{ k- 2}{2} \bigg)}$

By the given condition

$\displaystyle \sf{ \frac{ k- 2}{2} = - 1}$

$\displaystyle \sf{ \implies \: k - 2 = - 2}$

$\displaystyle \sf{ \implies \:k = 0}$

FINAL ANSWER

Hence the required point = ( 1 , 0 )

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