Given:
The coordinate of point R in quadrilateral RUST are (2,4).
R is dilated by a scale factor of 3, centered at the origin, followed by the translation [tex](x, y)\to (x+4,y)[/tex].
To find:
The coordinates of R' after dilation and translation.
Solution:
If a figure is dilated by a scale factor of 3, centered at the origin, then
[tex](x,y)\to (3x,3y)[/tex]
We value R(2,4).
[tex]R(2,4)\to R_1(3(2),3(4))[/tex]
[tex]R(2,4)\to R_1(6,12)[/tex]
The rule of translation is:
[tex](x, y)\to (x+4,y)[/tex]
Using this rule, we get
[tex]R_1(6,12)\to R'(6+4,12)[/tex]
[tex]R_1(6,12)\to R'(10,12)[/tex]
Therefore, the coordinates of point R' are (10,12) and the correct option is B.
