In this case, we can utilize the perpendicular bisector theorem, which states that \(\overline{SP}\cong\overline{PT}\). Therefore, set the measure of them equal to each other to figure out the unknown.
\(SP=PT\) | We know the length of these segments already. |
\(3m+9=5m-13\) | Subtract 2m from both sides first. |
\(9=2m-13\) | Add 13 to both sides. |
\(22=2m\) | Divide by 2 from both sides to isolate the variable completely. |
\(11=m\) | |
Using the same logic as before, we also know that \(\overline{SQ}\cong\overline{TQ}\).
\(SQ=TQ\) | Use substitution here! |
\(6n-3=4n+14\) | Subtract 4n from both sides. |
\(2n-3=14\) | Add 3 to both sides. |
\(2n=17\) | Divide by 2 from sides to isolate the unknown completely. This process is exactly the same as the first one. |
\(n=\frac{17}{2}=8.5\) | |
Go here https://web2.0calc.com/questions/not-sure-where-to-start-here to view my original response and the corresponding question.
I already explained in the previous post that opposite sides of a parallelogram are parallel by definition. Then, I encouraged you to try and figure out a relationship with two angles located on the same segment. In this case, \(\angle Z\) and \(\angle Y\) are same-side interior angles (sometimes referred to as consecutive interior angles). I know this because \(\overline{WZ}\parallel\overline{XY}\), and \(\overline{ZY}\) acts as the transversal. Because there is proof of parallel segments, we also know that the same-side interior angles are supplementary. If the angles are known to be supplementary, then the sum of the angles equals 180°. By the definition of supplementary angles, then, \(m\angle Z+M\angle Y=180^{\circ}\). Using the same logic as before, it is also possible to conclude that \(m\angle X+m\angle Y=180^{\circ}\). Based on the two previous conclusions, both \(\angle Z\) and \(\angle X\) are supplementary to a common angle, \(\angle Y\) in this case. When this occurs, the congruent supplements theorem states that \(\angle Z\cong\angle X\). Utilize this logic again to prove that the other pair of opposite angles, \(\angle W\text{ and }\angle Y\), are indeed congruent. The process is identical.
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