Points A and B are at (9 ,9 )(9,9) and (7 ,8 )(7,8), respectively. Point A is rotated counterclockwise about the origin by pi π and dilated about point C by a factor of 2 2. If point A is now at point B, what are the coordinates of point C?

1 Answer

Point C(-25, -26)C(25,26)

Explanation:

From A(9, 9)A(9,9)
point A will be at A'(x_a', y_a')=(-9, -9) after rotation of pi whether by counterclockwise or clockwise.

The formula for dilation with center of dilation C(x_c, y_c) by a factor k is
x_a''=k(x_a'-x_c)+x_c and y_a''=k(y_a'-y_c)+y_c

where (x_a'', y_a'') is the coordinates of the final position of A

Given that B is at (7, 8), therefore x_a''=7 and y_a''=8

The coordinates of C(x_c, y_c) can now be computed with k=2
x_a''=k(x_a'-x_c)+x_c
7=2(-9-x_c)+x_c
7=-18-2*x_c+x_c
7=-18-x_c
x_c=-25

And
y_a''=k(y_a'-y_c)+y_c
8=2(-9-y_c)+y_c
8=-18-2y_c+y_c
8=-18-y_c
y_c=-26

C(x_c, y_c)=(-25, -26)

God bless....I hope the explanation is useful.