Assalamualaikum warahmatullahi wabarakatuh Good morning spirit this time we will discuss about transformation geometry material the purpose of this learning is firstly it is hoped that students can analyze the properties of reflection with a coordinate approach secondly students can apply reflection rules in solving transformation problems there are four types firstly reflection or reflection secondly shift or translation thirdly multiplication or dilation fourthly rotation or rotation this time we will discuss about reflection or reflection ee Pay attention to this picture yes eah this is an example of reflection that you can find in everyday life a building is reflected by a river so the image of the building under the water surface is a shadow of the building above it so this water reflects yes this water is a mirror so we can conclude the definition of reflection is a geometric transformation in the form of moving the position of an object to the position of the reflection result with properties like a flat mirror reflection in plane geometry as a mirror can be used firstly the x axis secondly the y axis thirdly the line y = x the fourth line y = -x the fifth line y = n the keen line x = m and the 7th center point O 0,0 we will change one by one the first reflection on the x-axis of a point if it is reflected M this mirror or mirror will definitely get the shadow point here there is an example there is a point a this coordinate 5,3 will be reflected on the x-axis Yes yes the red x-axis means this is the mirror eah based on the properties of the mirror The distance from the point to the mirror with the shadow to the mirror is the same distance so there is here the shadow a' coordinate 5,-3 Okay there is a point a coordinate 5,3 reflected on the x-axis obtained a' 5,-3 note the origin point x is 5 the shadow x is also 5 remains while the origin point e is 3 now the shadow point y is -3 so the opposite so we can draw a conclusion if there is a point a coordinate x y reflected on the x-axis then the shadow Aak is x - ynya continue yes the second reflection on the y-axis we want to find the shadow point for example in remains the same there is a point a coordinate 5,3 we will reflect it on the y-axis of the mirror The red y-axis still has the same mirror properties The distance from the point to the mirror with the shadow to the mirror must be the same here five units That means here the coordinate is -5.3 Okay from this example if there is a point a 5.3 reflected on the y-axis we get a ak = -5.3 note 5 the original point x = 5 here the shadow is -5 the reverse or the opposite here the y is 3 the shadow y is also 3 remains so we can draw the conclusion if there is a point a x y reflected on the y-axis then we get -x y next the third reflection on the line y = x there is a point a coordinate 5.3 we will reflect it on the line y = x well this is the line y = x yes The distance of point A to the mirror must be the same as the distance of the shadow point to the mirror That means here the coordinate is 3.5 Okay from this example we pay attention to the original point X5 and here 3 so y this is the original point y 3 the shadow point 5 means it is reversed Okay D we conclude if AX y is reflected against the line y = x then its image a' is y x continue reflection against the line y = -x remains the same yes our point suppose there is a point a 5,3 line y = -x this is line y = -x Okay The distance of the point to the mirror must be the same as the distance of the image to the mirror so that the coordinates will be obtained here are -3, -5 so for example there is a point a 5,3 reflected against the line y = -x the image is obtained -3, -5 means here it is reversed and changes the sign Okay the conclusion is there is a coordinate x y is reflected against the line y = -x then a is -y -x continue reflection against the line y = n okay point a l coordinate is 5,3 for example we reflect it against the line y = 6 this is line y = 6 the distance from the mirror to the point is three units meaning here the image is here the coordinates are 5 9 5 comma point a 5,3 reflected against the line y = 6 6 obtained a' 5.9 9 this is obtained from 2 times the mirror mirror right y = 6 - 3 2 * mirror Given y- 3 2 * 6 12 - 3 so if we make a conclusion if there is a point a coordinate x y is reflected reflected on the line y = n then the image is x 2N - y further reflection on the line x = m is still the same yes for example we suppose there is a point a coordinate 5.3 we reflect on this line x = 1 yes seen the point with the mirror the distance is 4 units long then the distance of the image with the mirror is also 4 units H here the coordinate is -3.3 this so for example we suppose this x = 1 obtained -3.3 -3 this is obtained from 2 times the mirror minus X The original point abscissa at the origin 2 * 1 2 - 5 -3 -3.3 for y remains so we can draw a conclusion if there is a point a coordinate x y we reflect on the line x = M then the shadow a' is obtained is 2 * M minus x y then the reflection to the center O 0.0 remains the same, for example, there is a point a with coordinates 5.3 we reflect the mirror is the center is 0.0 here so the distance of point a with the mirror at 0.0 is how many units here then the shadow here is obtained the coordinate here is -5 -3 get this example for example there is a point a 5.3 reflected to the center 0.0 the shadow point a' is -5 -3 still only changes the sign Okay we can draw a conclusion if there is a point a x y reflected to the center O 0.0 then the shadow a' is -x - y yes next to understand this better pay attention to the first example example one Determine the shadow point a coordinates 3.4 if reflected to the x axis because we already have the formula earlier J is reflected to the x axis then the shadow becomes X - Y which changes The sign is y a 3.4 reflected to the x axis then Aak the shadow is obtained x remains 3 y changes sign 4 to -4 second example Determine the shadow of the line with the equation y = 5x + 3 reflected on the x-axis suppose x y is a point on the line y = 5x + 3 so we already know yes if there is a point min m that mirror mirror will definitely get the shadow x ' y ' yes here because it is reflected on the x-axis earlier it is known that the result if it is reflected on the x-axis is x -y meaning here yes meaning here here x ' is the same as X and y ' is the same - y x-nya Means the same as x' y-nya is the same as -y' reverse yes this is equation 1 x = x' both equations y = -y' substitute equation 1 and equation 2 to the line because we want to find the shadow equation here we replace y with -y ak x-nya we replace with x' both the left side and the right side we multiply -1 get y ' = -5x' -3 so the shadow is y = -5x - 3 finally the accent is removed question number 3 the shadow of the line 2x - y + 5 = 0 which is reflected on the line y = x is the same as for example there is x y is a point on the equation 2x - y + 5 = with 0 then if this point is reflected the shadow point will be obtained because this point is reflected on the line y = x then the shadow is y x means here x ' = y means here x ' = y and y is the same as x this is the first equation y = x ' the second equation X = y ' then substitute equation 1 and the DU equation to the line because we want to find the shadow equation so we replace x with y ' we replace y with x ' we get this if we move because this is still in one segment X in front -x + 2y -x' + 2yak + 5 = 0 so that the x is positive both the left and right areas we multiply -1 will get x ' - 2y ' -5 = 0 This is the last one, we just remove the accent mark, then the shadow equation is x - 2y - 5 = 0 That's all from me, hopefully it's useful and understandable. Next, please do the following questions, question 1. Determine the shadow of point a 3, -7 if it is reflected against the first x-axis B y-axis c Gis y = x D Gis y = -x and e origin o 0.0 second question Determine the shadow of the line y = 2x + 2 which is reflected against the origin o 0.0 third question Determine the equation of the curve y = x^ if it is reflected against the line x = 2 Thank you, peace be upon you warahmatullahi wabarakatuh