Question

1. figure hijkl is dilated by a scale factor of 6 with a center of dilation at the origin. the coordinates are h(1,1) i(2,2) j(3,3) k(4,4) l(5,5). what rule describes the dilation? (x,y)→( ) determine the new coordinates. h i j k l 9. the dilation of triangle abc using the origin as the center of dilation and a scale factor of 2 forms triangle def.

Explanation:

Step1: Recall dilation rule

For a dilation with scale - factor $k$ centered at the origin, the rule is $(x,y)\to(kx,ky)$. Here $k = 6$.

Step2: Apply the rule to find new coordinates of H

For point $H(1,1)$, using the rule $(x,y)\to(6x,6y)$, we get $H'(6\times1,6\times1)=(6,6)$.

Step3: Apply the rule to find new coordinates of I

For point $I(2,2)$, using the rule $(x,y)\to(6x,6y)$, we get $I'(6\times2,6\times2)=(12,12)$.

Step4: Apply the rule to find new coordinates of J

For point $J(3,3)$, using the rule $(x,y)\to(6x,6y)$, we get $J'(6\times3,6\times3)=(18,18)$.

Step5: Apply the rule to find new coordinates of K

For point $K(4,4)$, using the rule $(x,y)\to(6x,6y)$, we get $K'(6\times4,6\times4)=(24,24)$.

Step6: Apply the rule to find new coordinates of L

For point $L(5,5)$, using the rule $(x,y)\to(6x,6y)$, we get $L'(6\times5,6\times5)=(30,30)$.

Answer:

The rule: $(x,y)\to(6x,6y)$
$H'=(6,6)$
$I'=(12,12)$
$J'=(18,18)$
$K'=(24,24)$
$L'=(30,30)$