 Hello and welcome to the session. In this session, we will discuss that a given geometric figure and its image formed after transformation is a reflection or a translation or a rotation using angles, line segments, perpendicular lines, parallel lines and circles. Now we already know definitions of angles, circles, line segments and perpendicular lines. Let us define the transformations using these geometrical terms. First of all let us see reflection. Now we know that reflection of an object is obtained by flipping the object over the line of reflection. Now see the following figure. Here we can say that quadrilateral a dash b dash c dash d dash is image of quadrilateral a, b, c, d formed after reflection and here line l is the line of reflection. Now here we have two quadrilaterals. Now to see if a dash b dash c dash d dash is reflected image of the quadrilateral a, b, c, d. We draw a line segment joining the two corresponding points. Now here let us join b and b dash. Now here we have joined the points b and b dash. Similarly we can join the other points also. As here we have joined a and a dash c and c dash and we can also join d and d dash. Now here we see that line segment b, b dash intersects the vertical line l drawn with two figures at 90 degrees plus line segment b, b dash perpendicular if we join any other corresponding points then also that line segment will be perpendicular to the line l at the distance of point b from line l is equal to distance of point b dash from line l thus midpoint line segment b, b dash will lie on line action of line segment b, b dash and line l is the midpoint of line segment b, b dash. Thus the vertical line l is the line of reflection and quadrilateral a dash b dash c dash d dash is the reflected image of the given quadrilateral a, b, c, d. We can draw reflection of given figure in the line l by drawing the perpendicular from the given vertices and located where image points is equal. Thus we have to draw a reflection of this triangle a, b, c and l is the line of reflection. So here in the first step we will draw the perpendicular from the given vertices to the line and then we have located their image points such that the distance between the pre-image point and image point from line l is equal. Joining these image points we get the reflected image a dash b dash c dash. The given point that is pre-image lies on the line of reflection then is the point direction and here a translated figure will have same shape and size. A polygon is slided of given image in whether it is a translation or not. Now we see the following figure that polygon a dash b dash c dash d dash e dash is a translated image of polygon a, b, c, d, e. Also we see that the given polygon is sliding downwards in the direction in which given polygon is slided. Now here tells us the direction of the slide. We initially had this polygon that is the polygon a, b, c, d, e and when we slide it to three units right and one unit down in this direction it shows the direction of slide is the polygon a dash b dash c dash d dash e dash. Now an image is a translation of a given figure and of shape and its image are parallel. Now here we have joined the points d, d dash and the points a, a dash and d t dash are parallel to the line thus it is a translation of given figure and now let us discuss rotation. Now we know that rotation turns an object along the point in pure point direction that is to the right and negative angle shows that the pure point star and rotation moves the object to a circular point center through a specified angle. Now an image, the given object and its image rotation. Now suppose a is the given point and a dash is image point and p is center of rotation are rotated in a circle given by a center of rotation polygon by 90 degrees angle in anticlockwise direction. Now when we draw a circle with center o and radius o, c we see that the image also lies on the same circle. Now suppose we have given a triangle a, b, c and we have to draw its rotation about which mark c dash on 100 degrees angle and then in the next step mark c dash on 100 degrees line such that distance is equal to distance join r a and repeat the previous steps we can draw the image point c dash and then we will join these image points and join a dash b dash c dash we get a triangle are rotated in a circle with center r that point c dash also lies on the same circle c is equal to distance so we can say the point c and its image point c dash lie on the same circle c. We note that the point a and its image point a dash lie on the same circle c dash is equal to b and its image b dash lie on the same circle c double dash so distance r b is equal to distance therefore and triangle a dash b dash c dash these two triangles are equal so we must note that if we rotate the object of 140 degrees anticlockwise 60 degrees minus 140 degrees is equal to 220 degrees clockwise we have discussed definitions of rotations reflections and transformations in terms of angles and line segments and this completes the session the viewer have enjoyed the session