Question

list the coordinates of the vertices of figure abcd. original after dilation a(1, -1) ? b(1, -4) a(1, -2) c(3, -4) a(2, -2) d(3, -1) a(2, -1) a(2, 2)

Explanation:

Step1: Identify dilation rule

We need to find the rule for the dilation from the given original and dilated point $A(1, - 1)$ and $A'(1,-2)$. The $x$-coordinate of $A$ and $A'$ is the same ($x = 1$), and the $y$-coordinate of $A'$ is twice the $y$-coordinate of $A$ (since $-2=2\times(- 1)$). The dilation rule seems to be $(x,y)\to(x,2y)$.

Step2: Apply dilation rule to point $B$

For $B(1,-4)$, applying the rule $(x,y)\to(x,2y)$, we get $B'(1,2\times(-4))=B'(1, - 8)$.

Step3: Apply dilation rule to point $C$

For $C(3,-4)$, applying the rule $(x,y)\to(x,2y)$, we get $C'(3,2\times(-4))=C'(3,-8)$.

Step4: Apply dilation rule to point $D$

For $D(3,-1)$, applying the rule $(x,y)\to(x,2y)$, we get $D'(3,2\times(-1))=D'(3,-2)$.

Answer:

$A'(1,-2), B'(1,-8), C'(3,-8), D'(3,-2)$