Respuesta :
Given:
Point A (4, -3) is translated 3 units horizontally and -5 units vertically, rotated 90° clockwise, reflected over the x-axis, and dilated by a factor of 5.
To find:
The rule and coordinates of A'.
Solution:
Let a point be P(x,y).
If a point translated 3 units horizontally and -5 units vertically, then
[tex]P(x,y)\to P_1(x+3,y-5)[/tex]
Then, rotated 90° clockwise.
[tex](x,y)\to (y,-x)[/tex]
[tex]P_1(x+3,y-5)\to P_2(y-5,-(x+3))[/tex]
Then, reflected over the x-axis.
[tex](x,y)\to (x,-y)[/tex]
[tex]P_2(y-5,-(x+3))\to P_3(y-5,x+3)[/tex]
Dilated by a factor of 5.
[tex](x,y)\to (5x,5y)[/tex]
[tex]P_3(y-5,x+3)\to P'(5(y-5),5(x+3))[/tex]
[tex]P_3(y-5,x+3)\to P'(5y-25,5x+15)[/tex]
So, the rule of transformation is
[tex](x,y)\to (5y-25,5x+15)[/tex]
We have a point A(4,-3). So, put x=4 and y=-3.
[tex]A(x,y)\to A'(5(-3)-25,5(4)+15)[/tex]
[tex]A(x,y)\to A'(-15-25,20+15)[/tex]
[tex]A(x,y)\to A'(-40,35)[/tex]
Therefore, the coordinate of point A' are (-40,35).
