Question

quadrilateral hijk has vertices h(-1, 3), i(2, 3), j(2, -1), and k(-3, -1). it is dilated by a scale factor of 7 with a center of dilation at (0, 0). part a what are the coordinates of the image hijk? part b what is the algebraic representation of the dilation?

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor $k$ and center of dilation at the origin $(0,0)$, the rule is $(x,y)\to(kx,ky)$. Here $k = 7$.

Step2: Find coordinates of $H'$

Given $H(-1,3)$, then $H'=(7\times(-1),7\times3)=(-7,21)$.

Step3: Find coordinates of $I'$

Given $I(2,3)$, then $I'=(7\times2,7\times3)=(14,21)$.

Step4: Find coordinates of $J'$

Given $J(2, - 1)$, then $J'=(7\times2,7\times(-1))=(14,-7)$.

Step5: Find coordinates of $K'$

Given $K(-3,-1)$, then $K'=(7\times(-3),7\times(-1))=(-21,-7)$.

Step6: Write algebraic representation

The algebraic representation of the dilation with scale - factor $k = 7$ and center of dilation at the origin is $(x,y)\to(7x,7y)$.

Answer:

Part A: $H'(-7,21)$, $I'(14,21)$, $J'(14,-7)$, $K'(-21,-7)$
Part B: $(x,y)\to(7x,7y)$