Question

Could someone please explain this to me in detail? I am struggling with this problem on my homework.

K is the midpoint of LM. The coordinates of K are (3, 5) and the coordinates of L are (-5, -6), find the coordinates of M

Answer 1

you recall the mid-point formula, right?

Answer 2

vaguely.. could you re-explain it to me, please?

Answer 3

\(\bf \textit{middle point of 2 points }\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
L&({\color{red}{ -5}}\quad ,&{\color{blue}{ -6}})\quad M&({\color{red}{ M_x}}\quad ,&{\color{blue}{ M_y}})
\end{array}\qquad \\ \quad \\
\left(\cfrac{{\color{red}{ x_2}} + {\color{red}{ x_1}}}{2}\quad ,\quad \cfrac{{\color{blue}{ y_2}} + {\color{blue}{ y_1}}}{2} \right)\implies (3,5)
\\ \quad \\
\left(\cfrac{{\color{red}{ M_x}} + {\color{red}{ (-5)}}}{2}\quad ,\quad \cfrac{{\color{blue}{ M_y}} + {\color{blue}{ (-6)}}}{2} \right)\implies (3,5)
\begin{cases}
\cfrac{{\color{red}{ M_x}} + {\color{red}{ (-5)}}}{2}=3
\\ \quad \\
\cfrac{{\color{blue}{ M_y}} + {\color{blue}{ (-6)}}}{2}=5
\end{cases}\)

and solve for the missing coordinate there, in each case, to find the x,y coordinates of point M

Answer 4

So would it be 11, 16?

Answer 5

:)

Answer 6

yeap

Answer 7

thus M ( 11, 16)
x y

Answer 8

Awesome! Could you help me with another, please?

Answer 9

sure... just post anew...thus if I dunno. someone else may know and we can revise each other :)

Answer 10

OK :)