This problem requires knowledge of the midpoint formula. For any two coordinates, \((x_1,y_1)\) and \((x_2,y_2)\), the coordinate of their respective midpoint is located at \(\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)\).
Let's plug in those coordinates, shall we?
\(A(-1,9)\text{ and }B(3,8)\) | These are the coordinates given in the original problem. Let's use the formula to find the midpoint. |
\(\left(\frac{-1+3}{2},\frac{9+8}{2}\right)\) | Now, it is a matter of simplifying. |
\(\left(\frac{2}{2},\frac{17}{2}\right)\) | Since the question specifically asks for the coordinates to be written in a decimal format, I will do the conversion, albeit a simple one. |
\((1,8.5)\) | |
If you think about it, the midpoint formula (unlike others) should make sense logically; after all, all you are doing is finding the average of the given coordinates. If this is unclear, maybe this image will help facilitate your understanding of the midpoint formula. When I learned this formula, it definitely helped me.
Source: http://blog.brightstorm.com/wp-content/uploads/2015/04/midpoint31.jpg
\(\hspace{5mm}3x+7=5x+1\\ -3x\hspace{9mm}-3x\) | By subtracting 3x from both sides, I am getting closer to the solution of this equation. Subtracting 3x from both sides eliminates one term with an x in it. Since this is an equation, if you do something to one side, you must do the equivalent action to the other; otherwise, the equation is unbalanced! Remember that the goal is to isolate x and find its value. Note that this is not the only way to get rid of one of the x-terms. It is also possible to subtract 5x from both sides, but, by my own convention, I will keep the coefficient of the variable positive. |
\(\hspace{5mm}7=2x+1\\ -1\hspace{11mm}-1\) | By subtracting 1 from both sides, we are eliminating a constant term. This gets us ever so closer to isolating the variable. |
\(\hspace{5mm}6\hspace{3mm}=\hspace{5mm}2x\\ \div2\hspace{9mm}\div 2\) | Dividing by 2 on both sides allows us to finally isolate the variable, which is the ultimate goal of equations with unknowns. |
\(3=x\) | This is the only value for x that satisfies the original equation. |