Question

Line segment XY is located at X(2, 6) and Y(4,8). If the line segments is dilated by a scale factor of 2 with a center of dilation of T(-3, 4). What are the coordinates of X'?

Answer 1

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:

$(x,y)\to (k(x-a)+a,k(y-b)+b)$

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

$(x,y)\to (2(x-(-3))+(-3),2(y-4)+4)$

$(x,y)\to (2(x+3)-3,2y+2(-4)+4)$

$(x,y)\to (2x+6-3,2y-8+4)$

$(x,y)\to (2x+3,2y-4)$

The coordinate of X are (2,6).

$X(2,6)\to X'(2(2)+3,2(6)-4)$

$X(2,6)\to X'(4+3,12-4)$

$X(2,6)\to X'(7,8)$

Therefore, the coordinates of X' are (7,8).