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)=(}(x1+x2)/(2),\text{ }(y1+y2)/(2))`

Hence,

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

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

`\begin{gathered} 1=(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=(2+y2)/(2) \\ 5*2=2+y2 \\ 10=2+y2 \\ y2=10-2 \\ y2=8 \end{gathered}`

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