Question

find the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
a(-3, -5)
b(-1, 0)
c(-3, 5)
d(-4, 0)
drag & drop the answer
(-4, 0)
(-8, 0)
(-2, 0)
(-6, 10)

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale factor $k$, if a point has coordinates $(x,y)$, the new coordinates $(x',y')$ after dilation are given by $(x',y')=(k\cdot x,k\cdot y)$. Here $k = 2$.

Step2: Find new coordinates of point A

For $A(-3,-5)$, $x=-3,y = - 5$. Then $x'=2\times(-3)=-6$ and $y'=2\times(-5)=-10$. So the new coordinates of $A$ are $(-6,-10)$.

Step3: Find new coordinates of point B

For $B(-1,0)$, $x=-1,y = 0$. Then $x'=2\times(-1)=-2$ and $y'=2\times0 = 0$. So the new coordinates of $B$ are $(-2,0)$.

Step4: Find new coordinates of point C

For $C(-3,5)$, $x=-3,y = 5$. Then $x'=2\times(-3)=-6$ and $y'=2\times5 = 10$. So the new coordinates of $C$ are $(-6,10)$.

Step5: Find new coordinates of point D

For $D(-4,0)$, $x=-4,y = 0$. Then $x'=2\times(-4)=-8$ and $y'=2\times0 = 0$. So the new coordinates of $D$ are $(-8,0)$.

Answer:

$A(-3,-5)\to(-6,-10)$
$B(-1,0)\to(-2,0)$
$C(-3,5)\to(-6,10)$
$D(-4,0)\to(-8,0)$