Question

On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) and (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0). Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?

Answer 1

Answer:

$\dfrac{1}{3}$.

Step-by-step explanation:

In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).

In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula , we get

$QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6$

$Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2$

Now,  

$\text{Scale factor}=\dfrac{Q'R'}{QR}$

$\text{Scale factor}=\dfrac{2}{6}$

$\text{Scale factor}=\dfrac{1}{3}$

Therefore the scale factor is $\dfrac{1}{3}$.

Answer 2

Answer:

1/3

Step-by-step explanation:

Correct on edge!