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Find the coordinates of C if B is the Midpoint of AC.

B(1,6)

A(3,-2)

Midpoint of AB=(2,2)

 Apr 11, 2015

Best Answer 

 #1
avatar+354 
+10

To find the midpoint between 2 points, we can do $${\frac{\left({{\mathtt{x}}}^{{\mathtt{1}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{x}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}}}$$,$${\frac{\left({{\mathtt{y}}}^{{\mathtt{1}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{y}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}}}$$

So by inputting the coordinates you gave, $${\frac{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}{{\mathtt{2}}}} = {\mathtt{1}}$$,$${\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)}{{\mathtt{2}}}} = {\mathtt{6}}$$.

Then we can simply solve for x and y.

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{x}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}={\mathtt{2}}\\
{\mathtt{x}}=-{\mathtt{1}}\end{array}\right)} \Rightarrow {\mathtt{x}} = -{\mathtt{1}}$$

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{y}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}={\mathtt{12}}\\
{\mathtt{y}}={\mathtt{14}}\end{array}\right)} \Rightarrow {\mathtt{y}} = {\mathtt{14}}$$

So C= (-1,14)

 Apr 11, 2015
 #1
avatar+354 
+10
Best Answer

To find the midpoint between 2 points, we can do $${\frac{\left({{\mathtt{x}}}^{{\mathtt{1}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{x}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}}}$$,$${\frac{\left({{\mathtt{y}}}^{{\mathtt{1}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{y}}}^{{\mathtt{2}}}\right)}{{\mathtt{2}}}}$$

So by inputting the coordinates you gave, $${\frac{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}\right)}{{\mathtt{2}}}} = {\mathtt{1}}$$,$${\frac{\left({\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}\right)}{{\mathtt{2}}}} = {\mathtt{6}}$$.

Then we can simply solve for x and y.

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{x}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{x}}={\mathtt{2}}\\
{\mathtt{x}}=-{\mathtt{1}}\end{array}\right)} \Rightarrow {\mathtt{x}} = -{\mathtt{1}}$$

$$\underset{\,\,\,\,{\textcolor[rgb]{0.66,0.66,0.66}{\rightarrow {\mathtt{y}}}}}{{solve}}{\left(\begin{array}{l}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\small\textbf+\,}}{\mathtt{y}}={\mathtt{12}}\\
{\mathtt{y}}={\mathtt{14}}\end{array}\right)} \Rightarrow {\mathtt{y}} = {\mathtt{14}}$$

So C= (-1,14)

radio Apr 11, 2015
 #2
avatar+128083 
0

Nice one, radio.......!!!!!

 

 

  

 Apr 11, 2015

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