 Hello and welcome to the session. In this session we will discuss a question which says that drop of the algorithm with vertices minus 3 3 minus 3 minus 1 1 3 1 minus 1 and find the length of all its sides. Now before starting the solution of this question you should know some results. And the first result is if in a coordinate plane we have two points that is the first point a with coordinates x y 1 and the second point is b with coordinates x y 2 where x coordinate is fixed and y coordinate varies then the line segment joining these two points will be a vertical line and length of this line segment a b will be equal to absolute value of y 2 minus y 1. And secondly if in a coordinate plane we have two points that is the point a with coordinates x 1 y and the point b with coordinates x 2 y. Now here the x coordinate varies and y coordinate is fixed then the line segments joining these two points will be a horizontal line and length of this line segment a b will be equal to absolute value of x 2 minus x 1. Now these results will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now here we have to draw a problem with these four vertices. For plotting this we will take a coordinate plane in which horizontal axis is the x axis, vertical axis is the y axis. Now let us plot these four ordered pairs in this coordinate plane. First of all let us plot the ordered pair minus 3 3. Now where the x coordinate is negative y coordinate is positive so this ordered pair will lie in the second quadrant. So for plotting this ordered pair we will start from 0 as the x coordinate is negative that is minus 3 so we will move 3 units to the left of 0 and we will reach at this point then the y coordinate is positive that is 3 so we will move 3 units upwards and we will reach at this point which represents the ordered pair minus 3 3. Now we will plot the second ordered pair in which both x and y coordinates are negative which means this ordered pair will lie in the third quadrant. Now here this is the point which represents the ordered pair minus 3 minus 1. Now the third ordered pair will lie in the first quadrant as where both x and y coordinates are positive so this is the point which represents the ordered pair 1 3. Now the fourth ordered pair will lie in the first quadrant as here the x coordinate is positive and y coordinate is negative and this is the point which represents the ordered pair 1 minus 1. Now let us label these points as a b c and d where a represents the point minus 3 3 b represents the point minus 3 minus 1 c represents the point 1 minus 1 and d represents the point 1 3. Now let us join all these points consecutively that is a b b c c d d a. Now on joining all these points we are getting a polygon c c d and d a so it is a quadrant we have to find length of it. So for this we will use the results which are given to us in the key idea. So length of a b the coordinates of a r minus 3 3 and coordinates of b r minus 3 minus 1. Now here as the y coordinate varies so length of a b which is equal to absolute value of minus 1 minus 3 which is equal to absolute value of minus 1 which is equal to and y coordinate varies r to minus y 1 absolute value of 3 minus of minus 1 which is equal to absolute value of value of 4 which is equal to 4 units of b c and length of d a is a horizontal line where the x coordinate varies and y coordinate of b c will be equal to absolute value of x 2 minus x 1. So this is equal to 1 minus of minus 3 absolute value of 1 plus 3 which is equal to absolute value of 4 that is equal to the length of d a which is equal to absolute value of x 2 minus x 1. So this is equal to absolute value of minus 3 minus 1 which is equal to absolute value of minus 4 which is equal to 4 units a b c d b c which means both are equal that length of a length of d a similarly length of a b is same as length of d a question of the given question and that's all for the session hope you all have enjoyed the session.