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

ANSWER

A (-5, -1)

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:

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

where (x1, y1) = cordinates of A

(x2, y2) = cordinates of B

This means that:

$\begin{gathered} x\text{ = }\frac{x_1+x_2}{2} \\ \Rightarrow\text{ -2 = }\frac{1+x_2}{2} \\ \text{Cross multiply:} \\ 2\cdot\text{ -2 = 1 + }x_2 \\ -4\text{ = 1 + }x_2 \\ \Rightarrow\text{ }x_2\text{ = -4 - 1} \\ x_2\text{ = -5} \end{gathered}$

Also:

$\begin{gathered} y\text{ = }\frac{y_1+y_2}{2} \\ 0\text{ = }\frac{1+y_2}{2} \\ \text{Cross multiply:} \\ 0\cdot\text{ 2 = 1 + }y_2 \\ 0\text{ = 1 + }y_2 \\ \Rightarrow\text{ }y_2\text{ = -1} \end{gathered}$

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