Chapter 13.9, Problem 8ST2

To determine

To find: The coordinates of the point $J$ without introducing new letters.

Answer to Problem 8ST2

The coordinates of the point $J$ are $\left(c-g,h\right)$ .

Explanation of Solution

Given information:

The isosceles trapezoid is shown below:

  

Calculation:

As the given quadrilateral is a isosceles trapezoid. So, the projection of point $J$ on $x$ axis will be equidistant from the point $\left(c,0\right)$ as of the length of the projection of point with coordinates $\left(g,h\right)$ on $x$ axis from origin.

The projection of the point with coordinates $\left(g,h\right)$ on $x$ axis gives the coordinates $\left(g,0\right)$ .

The distance of the point with coordinates $\left(g,0\right)$ from the origin is equal to $g$ .

The projection of point $J$ on $x$ axis from the point $\left(c,0\right)$ gives the coordinates as $\left(c-g,0\right)$ .

As the point $J$ is $h$ units above the point with coordinates $\left(c-g,0\right)$ .

Therefore, the coordinates of the point $J$ are $\left(c-g,h\right)$ .