Question

AB has a line segment Mis the midpoint of AB A is the point (7,2) Mis the point (5,6) Work out the coordinate of B

Answer 1

Answer: B(3,10)

Explanation:

`A(7,2)\ \ \ \ M(5,6)\ \ \ \ B(Xb,Yb)=?`

The formula for calculating the coordinates of the middle of the segment with ends A(Xa, Ya) and B(Xb, Yb) in the plane:

`\displaystyle\\\boxed {Xm=(Xa+Xb)/(2)\ \ \ \ \ \ Ym=(Ya+Yb)/(2) }`

`\displaystyle\\\left \{ {{5=(7+Xb)/(2) \ \ \ \ (1)} \atop {6=(2+Yb)/(2)\ \ \ \ (2) }} \right. \ \ \ \`

Multiply equations (1) and (2) by 2:

`\displaystyle\\\left \{ {{10=7+Xb} \atop 12=2+Yb}} \right.\ \ \ \ \left \{ {{10-7=7+Xb-7} \atop {12-2=2+Yb-2}} \right. \ \ \ \ \left \{ {{3=Xb} \atop {10=Yb}} \right. \ \ \ \ \Rightarrow\ \\ \ B(3,10)`