 Hello and welcome to the session. In this session, we will discuss a question that says that transform a parallelogram having vertices p with coordinates 2, 3, q with coordinates minus 1, 0, r with coordinates minus 4, 0, and s with coordinates minus 1, 3 using the parallel transformations. And the first transformation is x y transforms to x plus 2 y minus 3. Second transformation is x y transforms to x. Also, we have to compare the two transformations with respect to distance preservation. Now let us start with the solution after given transformation. Now we have given a parallelogram other vertices q, r, and s on the graph. Now we have point p with coordinates 3. Then we have point q with coordinates minus 1, 0 with coordinates minus 4, 0, and lastly we have with coordinates minus 1, 3. Now let us join two q, then q parallelogram p, q, r, s using the given transformations. Now this is the first transformation. In the first transformation, x y transforms to y minus 3 and now let us find image of p, q using the given transformation rule. Now the point p has coordinates 2, 3, so putting and y is equal to 3 in the given transformation. The coordinates of image point 2 plus 2, 3 transforms to point p dash with coordinates is the image point of the point q with coordinates minus 1, 0 transforms to point q dash with coordinates minus 1 plus 2, that is 1 and 0 minus 3, that is minus 3. So the point q with coordinates minus 1, 0 transforms to the point q dash with coordinates 1 minus 3. Then point r with coordinates minus 4, 0 transforms to point r dash with coordinates minus 1, 3, point f dash with coordinates 1, these image points on the graph. Now the first point, then next point is q dash with coordinates minus 3. Now let us join p dash to q dash, then q dash to p dash as dash is 10 homeogram point image for part 1 and now let us start with in the second part we have the transformation given by x y transforms to x rule the image points Now here, now we have to find the image point of point B using this transformation rule. So putting x is equal to 2 and y is equal to 3 in this transformation we have the image point with coordinates to point B double dash with coordinates 2, 6, point Q with coordinates minus 1, 0, 2, 0, that is 0, then point R with coordinates minus 4, 0 transforms to point R double dash with coordinates minus 4, with coordinates minus 1, 3, transforms to point S double dash with coordinates minus 1 and S respectively. Put these image points on the graph. Now this is the point P double dash with coordinates 2, 6. This is the point Q double dash with coordinates minus 1, 0. This is the point R double dash with coordinates minus 4, 0 and lastly S double dash with coordinates minus 1, 6. Now joining all these points we get a parallelogram P double dash 2 double dash R double dash S double dash, which is the required image of the given parallelogram P double dash and now we have these consumations with respect to distance presentation. This image that is the parallelogram P dash Q dash R dash S dash and here we see the distance between the corresponding sides of two figures of distance formula If L is the point with coordinates x1, y1 is the point with coordinates x2, y2 then will be equal to square root of x1 whole square plus y2 minus y1 whole square. Distance between using distance formula. Now here we know in point Q has coordinates minus 1, 0 so let us find distance PQ using distance formula. Now in parallelogram PQ R is P as x1 y1 and coordinates of Q as x1. Now using distance formula, distance PQ is equal to square root of x1 minus 1 minus 2 whole square plus y2 minus y1 whole square that is 0 minus 3 whole square. This is equal to square root of minus 3 whole square plus 9 which is equal to square root of 18. Now S is a parallelogram so distance of parallelogram are equal so here distance is equal to distance PQ which is equal to square root of 18. Now from the graph we can see that Q R is horizontal that is the point Q and point Q is equal to you know that Q R is equal to the distance Q R which is equal to 3. Now we can see distance in the parallelogram P dash Q dash R dash S dash. Now here point Q dash has coordinates 1, 0 and point Q dash has coordinates 1 minus 3 is formula. Distance P dash Q dash is equal to square root of 0 whole square which is equal to whole square that is 9 plus minus 3 whole square that is 9. Which is equal to square root of 18. Now here again as P dash Q dash R dash S dash is a parallelogram so opposite sides are equal S dash is equal to distance P dash Q dash which is equal to square root of 18. So point Q dash and R dash are equal to 3 and this is equal to distance P dash S dash because opposite sides of parallelogram are equal so distance Q dash R dash is equal to distance S dash P dash is equal to 3. So from the two figures we find that corresponding figures are equal that is distance P dash Q dash distance Q R is equal to distance Q dash R is equal to distance. Reserves distance P dash Q dash R dash and S dash P dash using distance formula which R dash is 3. Distance S dash P dash dash is again 2 dash using distance formula. So using distance formula distance P dash Q dash is equal to 1 minus 2 dash 0 minus 6 whole square which is 9 plus minus 6 whole square which is 36 of 45. So R dash S dash dash is equal to S dash Q dash which is equal to square root of 45 PQ is not equal to distance P dash Q dash. Reserves distance increases the size of given parallelogram what we are telling is a radical strike and this is the solution of the given question hope you all have enjoyed the session.