Question

The midpoint of AB is M(-5, 1). If the coordinates of A are (-4,-5), what are

the coordinates of B?

Answer 1

Answer: B(-6,7)

Explanation:

M(-5, 1) A(-4,-5) B(x,y)=?

`\displaystyle\\M_x=(x_A+x_B)/(2) \\\\-5=(-4+x_B)/(2)\\\\`

Multiply both parts of the equation by 2:

`-5(2)=-4+x_B\\\\-10=-4+x_B\\\\-10+4=-4+x_B+4\\\\-6=x_B\\\\Thus,\ x_B=-6`

`\displaystyle\\\\\\1=(-5+y_B)/(2) \\\\`

Multiply both parts of the equation by 2:

`1(2)=-5+y_B\\\\2=-5+y_B\\\\2+5=-5+y_B+5\\\\7=y_B\\\\Thus,\ y_B=7`

Answer 2

-6, 7

Explanation: