Respuesta :
Given:
The point is (8,-9).
Rule of transformation [tex]R(90^\circ,0)\circ T<5,-2>[/tex].
To find:
The image of given point after transformation.
Solution:
Consider the give point is P(8,-9).
Rule of transformation [tex]R(90^\circ,0)\circ T<5,-2>[/tex] represents translation T<5,-2> after that rotation 90 degrees counter clockwise.
If a figure translated by T<5,-2>, then
[tex](x,y)\to (x+5,y-2)[/tex]
[tex]P(8,-9)\to P'(8+5,-9-2)[/tex]
[tex]P(8,-9)\to P'(13,-11)[/tex]
If a figure rotated 90 degrees counter clockwise, then
[tex](x,y)\to (-y,x)[/tex]
[tex]P'(13,-11)\to P''(-(-11),13)[/tex]
[tex]P'(13,-11)\to P''(11,13)[/tex]
Therefore, the image of point (8,-9) after transformation is (11,13).
The image of the point (8,-9) after the given transformation is (11,13) and this can be determined by using the rules of transformation.
Given :
Point - (8,-9)
The following steps can be used to determine the image of the point after transformation:
Step 1 - As per the given data translate the point (8,-9) by (5,-2).
[tex](x,y) \to (x+5,y-2)[/tex]
[tex]\rm P(8,-9) \to P'(13 , -11)[/tex]
Step 2 - Now, again as per the given data rotate the above points by [tex]90^\circ[/tex] counter-clockwise.
[tex]\rm P'(x,y)\to P"(-y,x)[/tex]
[tex]\rm P'(13,-11) \to P"(11,13)[/tex]
So, the image of the point (8,-9) after the given transformation is (11,13).
For more information, refer to the link given below:
https://brainly.com/question/15200241
