The graph shows a point at (4,1) and a line segment with endpoint at (2,2) and (6,2) This line segment will be dilated with the point of dilation at (4, 1) and a scale factor of 2. What is the 2-coordinate of
one of the endpoints of the dilated segment?

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MrRoyal MrRoyal · Answer 1 · 2022-02-15T13:17:18+01:00

Dilation involves changing the size of a figure

The endpoints of the image are (0,3) and (8,3)

The coordinates of the pre-image are give as:

(2,2) and (6,2)

The scale factor is given as:

k = 2

The center of dilation is given as:

(a,b) = (4,1)

The coordinates of the image are then calculated as:

(x,y) = (k(x -a) + a, k(y -b) + b)

For (2,2), we have:

[tex](x,y) \to (2(2 -4) + 4, 2(2 - 1) + 1)[/tex]

[tex](x,y) \to (0, 3)[/tex]

For (6,2), we have:

[tex](x,y) \to (2(6 -4) + 4, 2(2 - 1) + 1)[/tex]

[tex](x,y) \to (8, 3)[/tex]

Hence, the endpoints of the image are (0,3) and (8,3)