Question

(RLT.G.3.a, 1 pt) If the coordinates of A are (1, 1) and the midpoint of AB is (-2,0), determine the coordinates of other endpoint B. O A. (-5,-1) O B. (-0.5, 0.5) O C. (-1,0) O D. (0.5, 0.5)

Answer 1

A (-5, -1)

Step-by-step explanation

We see that the cordinates of A are (1, 1) and that of B are not given.

The midpoint of line AB between A and B is (-2, 0)

The midpoint of two points is given as:

`M(x,y)\text{ = (}(x_1+x_2)/(2),\text{ }(y_1+y_2)/(2))`

where (x1, y1) = cordinates of A

(x2, y2) = cordinates of B

This means that:

`\begin{gathered} x\text{ = }(x_1+x_2)/(2) \\ \Rightarrow\text{ -2 = }(1+x_2)/(2) \\ \text{Cross multiply:} \\ 2\cdot\text{ -2 = 1 + }x_2 \\ -4\text{ = 1 + }x_2 \\ \Rightarrow\text{ }x_2\text{ = -4 - 1} \\ x_2\text{ = -5} \end{gathered}`

Also:

`\begin{gathered} y\text{ = }(y_1+y_2)/(2) \\ 0\text{ = }(1+y_2)/(2) \\ \text{Cross multiply:} \\ 0\cdot\text{ 2 = 1 + }y_2 \\ 0\text{ = 1 + }y_2 \\ \Rightarrow\text{ }y_2\text{ = -1} \end{gathered}`

Therefore, the cordinates of the B are (-5, -1). That is Option A.