Chapter 13.8, Problem 4CE

To determine

To find:The missing coordinates without introducing any new letters.

Answer to Problem 4CE

The missing coordinates are $G\left(h+i,g\right),E\left(h,g\right)$ and $M\left(i,0\right)$ .

Explanation of Solution

Given information: In graph, GEOM is a parallelogram.

  

Since, M is on the x-axis.

So, y-coordinate of M is 0.

i.e., $M\left(i,0\right)$

In parallelogram, opposite sides are equal and parallel.

Here, $\text{OM || EG, OE || MG}$ and $\text{OM=EG, OE=MG}$

Since, point E and point G are on same height.

So, both points y-coordinates will same.

Y-coordinate of point G is g.

So, point $E\left(h,g\right)$ .

  $\begin{array}{l}EG=OM\\ EG=i\end{array}$

X-coordinate of point G is sum of x-coordinates of E and M

i.e.,

  $h+i$

So, $G\left(h+i,g\right)$ .

Hence, the missing coordinates are $G\left(h+i,g\right),E\left(h,g\right)$ and $M\left(i,0\right)$ .