Which rule represents a dilation with respect to the origin? d1.8(5, 10) = (9, 14) d1.8(5, 10) = (9, 18) d1.8(5, 10) = (13, 18) d1.8(5, 10) = (13, 26)

D1.8(5, 10) = (9, 18)

Step-by-step explanation:

It is required to find which rule represents a dilation with respect to the origin.

So, the corresponding value of x and and y should be in proportion and should be equal the dilation ratio.

Check the options to find the true rules:

1) D1.8(5, 10) = (9, 14)

9/5 = 1.8  , 14/10 = 1.4 ⇒ 9/5 ≠ 14/1 ⇒ Wrong rule

2) D1.8(5, 10) = (9, 18)

9/5 = 1.8  , 18/10 = 1.8 ⇒ 9/5 = 18/10 = 1.8 ⇒ True rule because of D1.8

3) D1.8(5, 10) = (13, 18)

13/5 = 2.6  , 18/10 = 1.8 ⇒ 13/5 = 18/10 ⇒ Wrong rule

4) D1.8(5, 10) = (13, 26)

13/5 = 2.6 , 26/10 = 2.6 ⇒ (13/5 = 26/10) but ≠ 1.8 ⇒ Wrong rule

So, The rule which represents a dilation with respect to the origin is:

D1.8(5, 10) = (9, 18)