Chapter 13.8, Problem 2CE

To determine

To find the missing coordinates in given figure. 

Answer to Problem 2CE

The missing coordinates are $M\left(2b,0\right)$

Explanation of Solution

Given information: $\Delta MON$ is isosceles and $N\left(b,c\right)$

  

Concept used:

In isosceles triangle two corresponding are equal.

Explanation: 

Vertex O of triangle is at origin so it has coordinates $\left(0,0\right)$

Also vertex M lies on x-axis. So, $y-coordinate$ of M is $0$

Now to find $x-coordinate$ of M

  $\Delta MON$ is isosceles, so we have $ON=NM$ , $O\left(0,0\right)\text{ and N}\left(b,c\right)$

  

This implies M can be labelled as $\left(2b,0\right)$ because height of isosceles triangle divides base into two equal halves.

So, x-coordinate of $M=$$b+b=2b$

Hence,

Missing coordinates of M are $\left(2b,0\right)$