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:
[tex]\displaystyle x_c=\frac{x+x'}{2}[/tex]
[tex]\displaystyle y_c=\frac{y+y'}{2}[/tex]
If the coordinates of the midpoint are given, then the endpoint P' can be found solving for x' and y':
[tex]x'=2x_c-x[/tex]
[tex]y'=2y_c-y[/tex]
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):
[tex]x'=2(-2)-(-5)=-4+5=1[/tex]
[tex]y'=2(5)-4=10-4=6[/tex]
The coordinates of B are (1,6)
