Given:
Line segment XY is located at X(2, 6) and Y(4,8).
The line segments is dilated by a scale factor of 2 with a center of dilation of T(-3, 4).
To find:
The coordinates of X'
Solution:
If a figure dilated by a scale factor k with a center of dilation (a,b), then the rule of dilation is:
[tex](x,y)\to (k(x-a)+a,k(y-b)+b)[/tex]
The line segments is dilated by a scale factor of 2 with a center of dilation of T(-3, 4). So, the rule of dilation is
[tex](x,y)\to (2(x-(-3))+(-3),2(y-4)+4)[/tex]
[tex](x,y)\to (2(x+3)-3,2y+2(-4)+4)[/tex]
[tex](x,y)\to (2x+6-3,2y-8+4)[/tex]
[tex](x,y)\to (2x+3,2y-4)[/tex]
The coordinate of X are (2,6).
[tex]X(2,6)\to X'(2(2)+3,2(6)-4)[/tex]
[tex]X(2,6)\to X'(4+3,12-4)[/tex]
[tex]X(2,6)\to X'(7,8)[/tex]
Therefore, the coordinates of X' are (7,8).
