Question

Find the correct algebraic representation of the dilation shown below.

a- (1/2x,1/2y)
b-(2/7x,2/7y)
c-(7/2x,7/2y)
d-(7x,7y)

Answer 1

Given:

The diagram of triangle DEF and triangle D'E'F' on a coordinate plan.

To find:

The algebraic representation of the dilation.

Solution:

The vertices of triangle DEF are D(0,7), E(7,-7) and F(-7,-7).

The vertices of triangle D'E'F' are D'(0,2), E(2,-2) and F(-2,-2).

We know that, the dilation factor is:

`k=\frac{x\text{ or }y\text{ coordinate of the dilated point}}{x\text{ or }y\text{ coordinate of the corresponding original point}}`

For point D' the y-coordinate is 7 and for point D the y-coordinate is 2. So,

`k=(2)/(7)`

The rule of dilation is:

`(x,y)\to \left(kx,ky\right)`

`(x,y)\to \left((2)/(7)x,(2)/(7)y\right)`

The algebraic representation of the dilation is
`\left((2)/(7)x,(2)/(7)y\right)`.

Therefore, the correct option is b.