Question

M is the midpoint of A and B. Find the A (Leave your answer with no spaces and use brackets and commas, use M and B as examples.)

M=(−2,0) B =(−5, 5)

Answer 1

A = (1,-5)

Explanation:

Let the midpoint of the two points A (x₁, y₁) and B(-5, 5) be M(2, 0)

Using the formula for calculating the midpoints of two coordinates

(X₁, Y₁) =
`(\frac{{x_1}+x_2}{2}, \frac{{y_1}+y_2}{2} )`

`X_1 = \frac{{x_1}+x_2}{2}\\Y_1 =\frac{{y_1}+y_2}{2}`

Given if (X₁, Y₁) is the midpoint, then X₁ = 2, Y₁ = 0

x₂ = -5 and y₂ = 5

Substituting this given values into the equation above to get the unknown coordinate;

`X_1 = \frac{{x_1}+x_2}{2}\\-2 = \frac{{x_1}-5\\}{2}\\-4 = x_1-5\\x_1=-4+5\\x_1 =1`

Similarly;

`Y_1 = \frac{{y_1}+y_2}{2}\\0 = \frac{{y_1}+5\\}{2}\\0 = y_1+5\\y_1=0-5\\y_1 =-5`

The coordinate of A = (1,-5)