Question

The point A(8,-6) is reflected over the point (1, 1) and its image is point B. Whatare the coordinates of point B?

Answer 1

In point reflection, the distance from the preimage to the point of reflection is the same as the distance from the point of reflection to the image.

Hence, this means that if the preimage coordinates are

$(x,y)$

and the image coordinates are

$(x\text{',y')}$

and are reflected over a point

$(a,b)$

It thus follows that

$\begin{gathered} a=\frac{x+x^{\prime}}{2} \\ \text{and} \\ b=\frac{y+y^{\prime}}{2} \end{gathered}$

From the question, the preimage is given as

$A=(x,y)=(8,-6)$

and it is reflected over the point

$(a,b)=(1,1)$

Applying the formula above, we can calculate the coordinates of the image B