 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that reflect a given figure in x-axis find the coordinates of the reflected image. We know that in reflection the point and its image are at the same distance from the line of reflection we also know that any coordinates say xy on reflection in x-axis becomes x-y. With this key idea let us proceed to the solution. In this question we are given a parallelogram a, b, c, d and we have to reflect it in x-axis. So we will first find the coordinates of each point. Here from the graph we see that a has coordinates minus 5, 3, b has coordinates minus 2, 3, c has coordinates minus 1, 1 and d is minus 4, 1. Now we will find image of each point in x-axis and from the key idea we know that in reflection the point and its image are at the same distance from the line of reflection and we know that any coordinates say xy on reflection in x-axis becomes x-y. Now from the graph we see that point c lies one unit above x-axis so its image will lie at the same distance of one unit below x-axis. We put a dot here and name it as c prime. Again point d is one unit above x-axis so its image will lie at the same distance of one unit below x-axis and exactly below point d. We put a dot and label it as d prime. Similarly point a is three units above x-axis so its image a prime will also be at the same distance below x-axis and will lie exactly in the line of point a so we put a dot here and label it as a prime. Again point b is also three units above x-axis so we plot its image at the distance of three units below x-axis exactly on the same line of point b. We put a dot here and name it as b prime. Now we join a prime to b prime, b prime to c prime, c prime to d prime and d prime to a prime and we get the required reflection of the given parallelogram. So reflection of parallelogram a, b, c, d is a parallelogram a prime, b prime, c prime, d prime. Now to find the coordinates of the given reflection that is a prime, b prime, c prime, d prime. We can find the coordinates from the coordinate plane. We are given that in parallelogram a, b, c, d we have point a with the coordinates minus five three, point b with the coordinates minus two three, point c with the coordinates minus one one and point d with the coordinates minus four one. In the reflection of parallelogram a, b, c, d that is in parallelogram a prime, b prime, c prime, d prime we have point a prime with the coordinates minus five minus three, point b prime with the coordinates minus two minus three, point c prime with the coordinates minus one minus one and point d prime with the coordinates minus four minus one. Also from the key idea we know that any coordinates say x, y on reflection in x axis becomes x minus y so here we can write we have point a prime with the coordinates minus five minus three that is point a with the coordinates minus five three on reflection in x axis becomes a prime with the coordinates minus five minus three similarly point b prime has the coordinates minus two minus three here we have point b with the coordinates minus two three which on reflection in x axis becomes b prime with the coordinates minus two minus three and similarly we have point c prime with the coordinates minus one minus one and point d prime with the coordinates minus four minus one. Hence we got the reflection of the parallelogram a, b, c, d as the parallelogram a prime, b prime, c prime, d prime with point a prime having coordinates minus five minus three point b prime with the coordinates minus two minus three point c prime with the coordinates minus one minus one and point d prime with the coordinates minus four minus one. This complete our session hope you enjoyed this session.