Question

The point A (−5,4) is reflected over the point (−2,5) and its image is point B. What are the coordinates of point B?

Answer 1

The coordinates of B are (1,6)

Explanation:

Point Reflection

Given the point P(x,y) and its reflection P'(x',y') with respect to the point C(xc,yc), C is the midpoint of the segment PP'.

This means the coordinates of C are:

`\displaystyle x_c=(x+x')/(2)`

`\displaystyle y_c=(y+y')/(2)`

If the coordinates of the midpoint are given, then the endpoint P' can be found solving for x' and y':

`x'=2x_c-x`

`y'=2y_c-y`

The point P' is the reflection of P over C.

We are given the coordinates of A(-5,4) and the point (-2,5). We need to find the coordinates of point B(x',y'). Let's use the formulas as if A was point P and C=(-2,5):

`x'=2(-2)-(-5)=-4+5=1`

`y'=2(5)-4=10-4=6`

The coordinates of B are (1,6)