Question

Triangle ABC has coordinates of A(-8, -8), B(4, -2), and C(2, 2). What are the coordinates of its image after a dilation centered at the origin with a scale factor of 1.5?

Answer 1

`(-12,-12),(6,-3)" and "(3,3)`

Explanation:

`"let A', B' and C' represent the image of A, B and C"`

`rArrvec(OA')=color(red)(1.5)vec(OA)`

`color(white)(rArrvec(OA'))=1.5((-8),(-8))=((-12),(-12))`

`rArrA'(-12,-12)`

`rArrvec(OB')=color(red)(1.5)vec(OB)`

`color(white)(rArrvec(OB'))=1.5((4),(-2))=((6),(-3))`

`rArrB'(6,-3)`

`rArrvec(OC')=color(red)(1.5)vec(OC)`

`color(white)(rArrvec(OC'))=1.5((2),(2))=((3),(3))`

`rArrC'(3,3)`

Answer 2

see explanation.

Explanation:

A dilation that creates a larger image is called an enlargement (scale factor `k > 1`).
A dilation that creates a smaller image is called a reduction (`0 < k < 1`).
After a dilation centered at the origin with a scale factor of `+k`,
a point `A(x,y) -> A'(kx,ky)`
given that `k=1.5`,
`=> A(-8,-8) -> A'(1.5xx(-8), " "1.5xx(-8))=A'(-12,-12)`
`B(4,-2) -> B'(1.5xx4, " "1.5xx(-2))=B'(6,-3)`
`=> C(2,2) -> C'(1.5xx2, " "1.5xx2)=C'(3,3)`