Question

2a: identify the vertices of this triangle.
the vertices of these triangle is
a=(3,2) b=(6,3.5) c=(8,0)
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

For a point \((x,y)\) dilated by a 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 \(x = 3\times\frac{1}{2}=\frac{3}{2}\), new \(y = 2\times\frac{1}{2} = 1\). So new \(A=(\frac{3}{2},1)\).

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

For \(B=(6,3.5)\), new \(x = 6\times\frac{1}{2}=3\), new \(y = 3.5\times\frac{1}{2}=1.75\). So new \(B=(3,1.75)\).

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

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

Answer:

The new vertices are \(A=(\frac{3}{2},1)\), \(B=(3,1.75)\), \(C=(4,0)\)