Question

draw the graph of $\triangle def$ after a dilation with center $(0,0)$ and scale factor 3.

choose the correct graph below.

$\bigcirc$ a.

$\bigcirc$ b.

$\bigcirc$ c.

click to select your answer and then click check answer.

Explanation:

Step1: Identify original triangle vertices

From the given graph, the vertices of $\triangle DEF$ are $D(0,0)$, $E(5,0)$, $F(0,5)$.

Step2: Apply dilation rule

Dilation with center $(0,0)$ and scale factor $k$ uses $(x,y)\to(kx,ky)$. For $k=3$:
$D'(3\times0, 3\times0)=(0,0)$
$E'(3\times5, 3\times0)=(15,0)$
$F'(3\times0, 3\times5)=(0,15)$

Step3: Match to options

The resulting triangle has vertices at $(0,0)$, $(15,0)$, $(0,15)$, which matches option C.

Answer:

C. (The graph with vertices at (0,0), (15,0), (0,15))