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

Answer:

The coordinates of B are (1,6)

Step-by-step 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:

$\displaystyle x_c=\frac{x+x'}{2}$

$\displaystyle y_c=\frac{y+y'}{2}$

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)