Question

Find the correct algebraic representation of the dilation shown below.

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:

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

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

$k=\dfrac{2}{7}$

The rule of dilation is:

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

$(x,y)\to \left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)$

The algebraic representation of the dilation is $\left(\dfrac{2}{7}x,\dfrac{2}{7}y\right)$.

Therefore, the correct option is b.