Question

2a: identify the vertices of this triangle. 2b: the triangle is being dilated by a factor of 1/2. what are the new vertices of this triangle? show all your work.

Explanation:

Step1: Recall the dilation formula

When a point \((x,y)\) is dilated by a scale factor \(k\), the new point is \((kx,ky)\). Here \(k = \frac{1}{2}\).

Step2: Apply the formula to point \(A\)

For \(A=(3,2)\), new \(x\) - coordinate \(=3\times\frac{1}{2}=\frac{3}{2}\), new \(y\) - coordinate \(=2\times\frac{1}{2} = 1\). So new \(A=(\frac{3}{2},1)\)

Step3: Apply the formula to point \(B\)

For \(B=(6,4)\), new \(x\) - coordinate \(=6\times\frac{1}{2}=3\), new \(y\) - coordinate \(=4\times\frac{1}{2}=2\). So new \(B=(3,2)\)

Step4: Apply the formula to point \(C\)

For \(C=(8,0)\), new \(x\) - coordinate \(=8\times\frac{1}{2}=4\), new \(y\) - coordinate \(=0\times\frac{1}{2}=0\). So new \(C=(4,0)\)

Answer:

The new vertices are \(A = (\frac{3}{2},1)\), \(B=(3,2)\), \(C=(4,0)\)