Chapter 6.6, Problem 3CYP

To determine

To calculate: To find the x-coordinate of point G

Answer to Problem 3CYP

x-coordinate of point G is $10.5$

Explanation of Solution

Given: Trapezoid ABCD shown below, $\overline{FG}$ is parallel to $\overline{AD}$

  

Formula Used:

Coordinates of mid-point of side having points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ is calculated as follows:

  $\left(x^{\prime },y^{\prime }\right)=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}$

Calculation:

Trapezium is given as follows:

  

In above figure, point F is mid-point of side AB

Also, given that $\overline{FG}$ is parallel to $\overline{AD}$

Thus, line FG is bisects the side CD, i.e. G is mid-point of side CD

Therefore, coordinates of mid-point of CD is calculated as follows:

  $\begin{array}{l}G\left(x^{\prime },y^{\prime }\right)=\frac{20+1}{2},\frac{0+4}{2}\\ G\left(x^{\prime },y^{\prime }\right)=\frac{21}{2},\frac{4}{2}\\ G\left(x^{\prime },y^{\prime }\right)=10.5,2\end{array}$

Conclusion:

Hence, x-coordinate of point G is $10.5$