Question

C lies at (1,5) and is the midpoint of AB. If A is at (3,2), find the coordinate for point B.(-1.8)(8.-1)(5.-1)(60)

Answer 1

Given:

The coordinates of C, the midpoint of AB, (X, Y)=(1, 5).

The coordinates of A, (x1, y1)=(3, 2).

Let the coordinates of B be (x2, y2).

The midpoint formula is given by,

$(X,\text{ Y)=(}\frac{x1+x2}{2},\text{ }\frac{y1+y2}{2})$

Hence,

$\begin{gathered} X\text{=}\frac{x1+x2}{2}\text{ ---(1)} \\ Y=\frac{y1+y2}{2}\text{ ---(2)} \end{gathered}$

Substitute the known values in equation (1) and solve for x2.

$\begin{gathered} 1=\frac{3+x2}{2} \\ 2=3+x2 \\ x2=2-3 \\ x2=-1 \end{gathered}$

Hence, x2=-1.

Substitute the known values in equation (2) and solve for y2.

$\begin{gathered} 5=\frac{2+y2}{2} \\ 5\times2=2+y2 \\ 10=2+y2 \\ y2=10-2 \\ y2=8 \end{gathered}$

Therefore, the coordinates of point B is (x2,y2)=(-1, 8).