Chapter 13.8, Problem 1CE

To determine

To find the missing coordinates in given figure. 

Answer to Problem 1CE

The missing coordinates are $P\left(0,a\right)\text{,}T\left(a,a\right)$

Explanation of Solution

Given information: $POST$ is a square.

  

Concept used:

Square has all sides equal.

Explanation: 

From figure we have vertex of square that are P,O,S,T. Since vertex O lies at origin so its coordinates are $\left(0,0\right)$

Also given $S\left(a,0\right)$

Now to find coordinates of T and P

Moving from origin to vertex S clearly distance is $a$

Therefore,

OS= $a$

Since square has all sides equal so,

  $PO=OS=ST=TP=a$

Vertex P is lying on $y$ -axis so clearly its $x$ -coordinate is $0$ and distance from Origin to vertex P is $a$

Therefore,

Coordinates of point P are $\left(0,a\right)$

Now to find coordinates of T

From figure,

  

Vertical distance from vertex S lying on $x$ -axis to vertex T is $a$ because ST= $a$ . So $y\text{ coordinate}$ of T is $a$

Horizontal distance from vertex P lying on $y$ -axis to vertex T is $a$ because TP= $a$ .So $x$ coordinate of T is $a$

Hence,

Coordinates of T are $\left(a,a\right)$

Thus,

Missing coordinates $P\left(0,a\right)\text{ and T}\left(a,a\right)$