Question

no additional details were added for this assignment. graph the image of the given triangle under a dilation with a scale factor of 1/4 and center of dilation (0, 0). to graph the triangle, select the \polygon\ tool and draw the triangle by plotting each vertex in order until it lands back on the first vertex. do not retrace any sides. you may use the \move\ tool to move your image if needed. polygon + move undo redo × reset

Explanation:

Step1: Recall dilation formula

If a point $(x,y)$ is dilated with a scale - factor $k$ and center of dilation at the origin $(0,0)$, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$.

Step2: Identify vertices of the given triangle

Let's assume the vertices of the given triangle are $(0,4)$ and $(8,1)$.

Step3: Calculate new vertices

For the vertex $(0,4)$ with $k = \frac{1}{4}$, we have $x'=\frac{1}{4}\times0 = 0$ and $y'=\frac{1}{4}\times4 = 1$.
For the vertex $(8,1)$ with $k=\frac{1}{4}$, we have $x'=\frac{1}{4}\times8 = 2$ and $y'=\frac{1}{4}\times1=\frac{1}{4}$.
The third vertex is the origin $(0,0)$ which remains the same after dilation with center at the origin.

Step4: Plot the new triangle

Use the "Polygon" tool to plot the new triangle with vertices $(0,1)$, $(2,\frac{1}{4})$ and $(0,0)$ in order until it lands back on the first vertex.

Answer:

Use the above - calculated vertices to graph the dilated triangle using the given tools.