Question

Find the image of the point A (5,-3) under reflection in the point P (-1,3).

Answer 1

Answer:

(-7,9)

Step-by-step explanation:

(5+x)/2=-1,(3+y)/2=3

x=-7,y=9

Answer 2

Answer:

The image would be (-7, 9)

Step-by-step explanation:

Given,

The point of reflection P (-1, 3),

Let the image of a point A(5, -3) is A'(x, y) under the reflection in the point P,

Since, the distance of a point from the point of reflection is same as the distance of its image from the point of reflection,

That is,

P is the midpoint of the segment joining A and A',

$(\frac{5+x}{2}, \frac{-3+y}{2})=(-1, 3)$

Comparing x-coordinates,

$\frac{5+x}{2}=-1$

$5+x=-2$

$\implies x = -7$,

Comparing y-coordinates,

$\frac{-3+y}{2}=3$

$-3+y=6$

$\implies y = 9$

Hence, the image of A would be A'(-7, 9)