Question

let p be the midpoint of AB. Find the coordinates of A, Given the coordinates of P and B
1. B(-1,3) P(2,2)

Answer 1

@jdoe0001

Answer 2

\(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
A&({\color{red}{ a_x}}\quad ,&{\color{blue}{ a_y}})\quad B&({\color{red}{ -1}}\quad ,&{\color{blue}{ 3}})
\end{array}\qquad
\left(\cfrac{{\color{red}{ -1}} + {\color{red}{ a_x}}}{2}\quad ,\quad \cfrac{{\color{blue}{ 3}} + {\color{blue}{ a_y}}}{2} \right)=(2,2)\ P
\\ \quad \\
thus\to
\begin{cases}
\cfrac{{\color{red}{ -1}} + {\color{red}{ a_x}}}{2}-2
\\ \quad \\
\bf \cfrac{{\color{blue}{ 3}} + {\color{blue}{ a_y}}}{2}=2
\end{cases} \)

Answer 3

hmmm shoot a minus typos anyhow if point P is (2,2) that means \(\bf thus\to
\begin{cases}
\cfrac{{\color{red}{ -1}} + {\color{red}{ a_x}}}{2}=2
\\ \quad \\
\bf \cfrac{{\color{blue}{ 3}} + {\color{blue}{ a_y}}}{2}=2
\end{cases} \)

Answer 4

and you can just solve for \(\bf a_x\ and \ a_y\) to find the coordinates of A

Answer 5

(-1+a)/2 =2?? i don't get it

Answer 6

well... lemme call those 2 guys ... a different name then.. "a" and b"

so we can find the coordinates (a,b) for point A

so \(\large thus\to
\begin{cases}
\cfrac{{\color{red}{ -1}} + {\color{red}{ a}}}{2}=2\to &{\color{red}{ a}}=\square ?
\\ \quad \\
\cfrac{{\color{blue}{ 3}} + {\color{blue}{ b}}}{2}=2\to &{\color{blue}{ b}}=\square ?
\end{cases} \)

Answer 7

ooooooh, xD just me being an idiot. xD a=5 b=1

Answer 8

yeap thus A = (5,1)