My topic is Geometry

Question

Point A is (-7, 5) and point M is at (0, 4)

Point M is the midpoint of point A and Point B

What are the coordinates of point B

Answer 1

For a midpoint

(x1+x2)/2 = x

(y1+y2)/2 = y

Plugging in the values given and solve

(-7+x2)/2 = 0 Multiply both sides by 2

-7+x2 = 0 Add 7 to both sides

x2 = 7

(5+y2)/2 = 4 Multiply both sides by 2

5+y2 = 8 Subtract 5 from both sides

y2 = 3

The other point is (7,3)

Answer 2

Hi Bry,

Given two points A(x₁ , y₁) and B(x₂ , y₂). The midpoint M between A and B is ( (x₁ + x₂) / 2 , (y₁ + y₂) / 2 ).

Since we know the point A (-7,5) and midpoint M(0,4), by using the formula above, we have

(x₁ + x₂) / 2 = ((-7) + x₂) / 2 = 0 which implies that x₂ = 7.

Similar,

(y₁ + y₂) / 2 = (5 + y₂) / 2 = 4 which implies that y₂ = 3.

So, the coordinates of point B are B = (7,3).

Best,