Question

the figure below is dilated by a factor of $\frac{3}{4}$ centered at the origin. plot the resulting image. click twice to plot a segment. click a segment to delete it.

Explanation:

Step1: Identify the coordinates of the vertices

The vertices of the original triangle are \(V(- 4,0)\), \(X(-4,4)\) and \(W(4,0)\).

Step2: Apply the dilation formula

The dilation formula for a point \((x,y)\) centered at the origin with a scale - factor \(k\) is \((kx,ky)\). Here \(k = \frac{3}{4}\).
For point \(V(-4,0)\):
\(x=-4,y = 0,k=\frac{3}{4}\), then the new coordinates \(V'=(\frac{3}{4}\times(-4),\frac{3}{4}\times0)=(-3,0)\)
For point \(X(-4,4)\):
\(x=-4,y = 4,k=\frac{3}{4}\), then the new coordinates \(X'=(\frac{3}{4}\times(-4),\frac{3}{4}\times4)=(-3,3)\)
For point \(W(4,0)\):
\(x = 4,y=0,k=\frac{3}{4}\), then the new coordinates \(W'=(\frac{3}{4}\times4,\frac{3}{4}\times0)=(3,0)\)

Step3: Plot the new points

Plot the points \(V'(-3,0)\), \(X'(-3,3)\) and \(W'(3,0)\) and connect them to form the dilated triangle.

Answer:

Plot the points \((-3,0)\), \((-3,3)\) and \((3,0)\) and connect them.