Question

Edwin was trying to find the missing endpoint of segment AB he was given the following point a is located at -4,2 and the midpoint is -7,5!where is point b located

Answer 1

The correct answer is the first option: (-10, 8)

Step-by-step explanation:

For two given points that form a segment, P and Q, we can find the coordinates of the midpoint using:

`\begin{gathered} \begin{cases}P=(x_P,y_P){} \\ Q={(x_Q},y_Q)\end{cases} \\ . \\ Midpoint=(x_M,y_M),\text{ }where: \\ . \\ x_M=(x_P+x_Q)/(2) \\ . \\ y_M=(y_P+y_Q)/(2) \end{gathered}`

We know that A = (-4, 2) and the midpoint = (-7, 5). Then;

`\begin{gathered} B=(x_B,y_B) \\ . \\ -7=(-4+x_B)/(2) \\ . \\ 5=(2+y_B)/(2) \end{gathered}`

And solve the two equations:

`\begin{gathered} -7=(-4+x_B)/(2) \\ . \\ -7\cdot2=-4+x_B \\ -14+4=x_B \\ x_B=-10 \end{gathered}`
`\begin{gathered} 5=(2+y_B)/(2) \\ . \\ 5\cdot2=2+y_B \\ 10-2=y_B \\ y_B=8 \end{gathered}`

Thus, B = (-10, 8)