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),(3,3)`

Explanation:

`"Since the centre of dilatation is the origin to obtain"`
`"the images of the given points we only require to"`
`"multiply the coordinates of the original points "`
`"by the scale factor"`

`A'=(-8xx1.5),(8xx1.5)=(-12,12)`

`B'=(4xx1.5),(-2xx1.5)=(6,-3)`

`C'=(2xx1.5),(2xx1.5)=(3,3)`

Answer 2

New coordinates of A, B, C are

`(-12,12), (6,-3), (3,3)` respectively.

Explanation:

`A(-8,8), B (4, -2), C (2,2), O (0,0)`

Dilated by factor d = 1.5 about origin#

`A’ ((x),(y)) = d * A ((x),(y)) - (d-1) * O ((x),(y))`

`A’((x),(y)) = 1.5* ((-8),(8)) - 0.5 * ((0),(0))`

Coordinates of `A’(x,y) = (-12, 12)`

Similarly coordinates of B’(x,y) = (1.54, 1.5-2) = (6,-3)#

`C’(x,y) = (1.5*2, 1.5*2) = (3,3)`