Chapter 13, Problem 17CT

To determine

To find: The missing coordinates of the given isosceles trapezoid.

Answer to Problem 17CT

The missing coordinates of the isosceles trapezoid is $\left(f-g,h\right)$ .

Explanation of Solution

Given information: The figure of isosceles trapezoid is:

  

Three vertex of isosceles trapezoid are $\left(0,0\right),\left(f,0\right)\text{ and }\left(g,h\right)$ .

Calculation:

Consider the points on the coordinate plane as shown below:

  

It is known that a pair of opposite sides of isosceles trapezoid is parallel. In the given figure OA is parallel to BC.

Given that the coordinates of point B is $\left(g,h\right)$ . The y -coordinate of point C is the same as the y -coordinate of point B. So, the y -coordinate of point C is $h$ .

Calculate length of AB.

  $\begin{array}{l}\text{EA}=\text{OA}-\text{OE}\\ \text{EA}=\left(f-g\right)\end{array}$

Since, it is an isosceles trapezoid. So,

  $\begin{array}{l}\text{EA}=\text{OD}\\ \text{EA}=\left(f-g\right)\end{array}$

The coordinate of D is $\left(\left(f-g\right),0\right)$ .

Now, the x -coordinate of C and D will be the same. So, the x -coordinate of C is $\left(f-g\right)$ .

Therefore, the missing coordinates of the isosceles trapezoid is $\left(f-g,h\right)$ .