Question

write the coordinates of the vertices after a dilation with a scale factor of \\(\frac{1}{2}\\), centered at the origin.
\\(a(\square, \square)\\)
\\(b(\square, \square)\\)
\\(c(\square, \square)\\)

Explanation:

Step1: Find original coordinates

From the graph, \(A(-4,-6)\), \(B(0,-6)\), \(C(0,-10)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = \frac{1}{2}\), the formula is \((x,y)\to(kx,ky)\)

• For \(A(-4,-6)\): \(A'(\frac{1}{2}\times(-4),\frac{1}{2}\times(-6))=(-2,-3)\)
• For \(B(0,-6)\): \(B'(\frac{1}{2}\times0,\frac{1}{2}\times(-6))=(0,-3)\)
• For \(C(0,-10)\): \(C'(\frac{1}{2}\times0,\frac{1}{2}\times(-10))=(0,-5)\)

Answer:

\(A'(-2,-3)\), \(B'(0,-3)\), \(C'(0,-5)\)