218k views
0 votes
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?

The point A (−5,4) is reflected over the point (−2,5) and its image is point B. What-example-1
User Wachr
by
7.9k points

1 Answer

4 votes

Answer:

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)

User Ncuillery
by
9.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories