 Hello and welcome to the session. In this session we will learn how to draw polygons in a coordinate plane and how to find the length of a size drawing vertices having same x coordinate or y coordinate. First of all, let us learn how to draw polygons in the coordinate plane when coordinates of vertices are given. Now in our earlier sessions we have learnt to plot ordered pairs in the coordinate plane. Also we know that polygons are plane figures or we can say polygons are two-dimensional figures having three or more sides and all sides are straight lines. For example, a triangle is a polygon with three sides, a coordinate is a polygon with four sides and a pentagon is also a polygon with five sides and so on. Now consider three ordered pairs, two, one, two, three. Now let us plot these ordered pairs on a graph for a pair on the graph. The x and y coordinates both are positive. So this point will lie in the first quadrant. So here this is the point which represents the ordered pair two, one and similarly we will plot the other two ordered pairs also. Now where this is the point which represents the ordered pair two, three. This is the point which represents the ordered pair four. So we have plotted the three ordered pairs in a coordinate plane. Now let us name these points as A, B. The point A represents the ordered pair two, three. Point B represents the ordered pair two, one and point C represents the ordered pair four, two. Now let us join these points consecutively that is A, B, B, C. Now on joining these points we catch the shape of a triangle which is a polygon with three sides A, B, B, C and C, A. Also A, B and C are the three vertices of the triangle A, B, C. Now let us draw a polygon in a coordinate plane having vertices minus 3, 3, 1, 3, 1, 0 and minus 3, 0. For this let us plot these four vertices in this coordinate plane and let us plot the ordered pair minus 3, 3 in the coordinate plane. Now here the x coordinate is negative whereas the y coordinate is positive. It means that this point will lie in the second coordinate. Now here as x coordinate is negative. So from 0 we will move three minutes to the left of 0 and we will reach at this point. Then y coordinate is 3 which is positive. So from this point we will move three minutes upwards and this is the point which represents the ordered pair minus 3, 3. Now let us plot the second ordered pair in which the x and y coordinates both are positive which means that this point will lie in the first coordinate. Now here this is the point whose x coordinate is 1 and y coordinate is 3. Now let us plot the third ordered pair which is 1, 0. Now here the x coordinate is 1 so we will start from 0 and move one unit to the right of 0 and we will reach at this point. Now here the y coordinate is 0 which means we do not move any unit up or down. So we will stay at this point and this is the point whose x coordinate is 1 and y coordinate is 0. We will plot the fourth ordered pair which is minus 3, 0. So this is the point whose x coordinate is minus 3 and y coordinate is 0. Now let us name these points as A, B, C. Here we always label the points consecutively like A, B, C, D or A, D, C, B. Now let us join these points consecutively that is A, B, C, D, D, A. Now this is a polygon with four sides A, B, C, C, D and D, A. So it is a four-sided polygon which means A, B, C, D is a quadrilateral. Now let us see how to find the length of a side joining vertices having same x coordinate or same y coordinate. Now here consider two points A and B with same x coordinate. Now where the x coordinate of both these points is 2 and where the y coordinate varies. Now let us plot these points on a coordinate plane. Now here the coordinates 2, 3, B whose coordinates are 2 and 1. Now on joining these points you can see that we get a vertical straight line same x coordinates. Now let us plot these two points on a coordinate plane. Now here this is the point C whose coordinates are minus 4, 1 and this is the point D whose coordinates are minus 4, minus 2. Now again on joining these points we will get a vertical straight line. This means whenever the x coordinate is fixed and y coordinate varies. Then the line joining these two points is a vertical line and now consider two points with same y coordinate. Now here the y coordinate is same that is 5 and the x coordinate varies. Now let us plot these points on a coordinate plane. Now here you can see this is the point E whose coordinates are 1 and 5. This is the point F with coordinates 4 and 5. Now on joining these two points we get a horizontal line. Whenever the y coordinate is fixed and it varies in the ordered pairs then the line joining such points will be horizontal. Now on the graph length means distance between the two ordered pairs. Now from the graph we can find the length of line segments AB, CT and AF. Now AB is formed by joining the points A and B whose x coordinate is same and y coordinate varies. And here the change in y coordinate is the difference between the y coordinates which is 3 minus 1 that is equal to 2. So length of AB is equal to 2 units. The coordinate x y 1 coordinates x y 2 that is the x coordinate is same and y coordinate varies these two points. The length of AB is equal to the change in y coordinate which is y 2 minus y 1. Now as the length is always positive so for finding out the length of AB we will take y 2 minus y 1. Now we can find length of CD which is equal to absolute value of y 2 minus y 1 which is equal to absolute value of minus 2 minus 1 which is equal to absolute value of minus 3 which is equal to 3. So length of CD is 3 units. Now for the line segment EF the x coordinate varies so for finding out the length of EF we will put the change in the x coordinate. So here the change in x is equal to the difference in the x coordinate which is 4 minus 1 which is equal to 3. So length of EF is equal to 3 units with coordinates x 1 y and point B with coordinates x 2 y that is where the x coordinate varies and y coordinate is fixed. Line segment joining these two points will be equal to the change in x coordinate which is equal to x 2 minus x 1 which is always positive. So we will take the absolute value of x 2 minus x 1 for finding out the length of AB. Now let us find the length of the sides AB, BC, CD and TA. From the given graph let us find the length of AB. Now here for the points A and B the x coordinate is fixed whereas it varies. So length of AB will be equal to the absolute value of y 2 minus y 1 which is equal to absolute value of 0 minus 3 which is equal to absolute value of minus 3 which is equal. Now let us find the length of BC times B and C the y coordinate is same. So length of BC will be equal to absolute value of x 2 minus x 1 which is equal to absolute value of 1 minus of minus 3 absolute value of 1 plus 3 which is equal to absolute value of 4 that is equal to. Now let us find the length of CD and y coordinate varies. So length of CD will be equal to absolute value of 3 minus 0 which is equal to absolute value of 3 which is equal to 3 unit. For the points B and A y for the length of TA will be equal to absolute value of minus 3 minus 1 which is equal to absolute value of minus 4 which is equal to. Remember one thing that whether we take the length of AB or BA it is the same thing as here by taking the absolute values we are getting the same results for the length of AB or length of PA. So in this session we have learnt in a coordinate plane and how to find the length of the side joining vertices having same x coordinate or same y coordinate. This completes our session. Hope you all have enjoyed the session.