Question

the figure below is dilated by a factor of 3 centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Identify original coordinates

First, we need to find the coordinates of the vertices of the original triangle. Let's assume the original vertices are:

• \( V(-2, 0) \) (from the graph, looking at the x and y axes)
• \( U(3, 0) \) (on the x - axis)
• \( T(0, -2) \) (on the y - axis)

Step2: Apply dilation rule

The rule for dilation centered at the origin with a scale factor \( k \) is \( (x,y)\to(kx,ky) \). Here, \( k = 3 \).

For point \( V(-2,0) \):
Multiply each coordinate by 3. So \( V'=(3\times(-2),3\times0)=(-6,0) \)

For point \( U(3,0) \):
Multiply each coordinate by 3. So \( U'=(3\times3,3\times0)=(9,0) \)

For point \( T(0, -2) \):
Multiply each coordinate by 3. So \( T'=(3\times0,3\times(-2))=(0, -6) \)

Step3: Plot the new points

Now, we plot the points \( V'(-6,0) \), \( U'(9,0) \), and \( T'(0, -6) \) on the coordinate plane and connect them to form the dilated triangle.

Answer:

The dilated triangle has vertices at \( (-6,0) \), \( (9,0) \), and \( (0, -6) \). To plot the image, mark these three points on the coordinate grid and draw the sides between them.