Question

graph the image of △qrs after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

Let \(Q=(0,0)\), \(R = (2,0)\), \(S=(0, - 2)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 4\), the formula for a point \((x,y)\) is \((x',y')=(k\cdot x,k\cdot y)\)
For \(Q=(0,0)\): \(Q'=(4\times0,4\times0)=(0,0)\)
For \(R=(2,0)\): \(R'=(4\times2,4\times0)=(8,0)\)
For \(S=(0, - 2)\): \(S'=(4\times0,4\times(-2))=(0,-8)\)

Step3: Graph the new triangle

Plot the points \(Q'=(0,0)\), \(R'=(8,0)\) and \(S'=(0,-8)\) and connect them to form \(\triangle Q'R'S'\)

Answer:

Plot the points \(Q'=(0,0)\), \(R'=(8,0)\) and \(S'=(0,-8)\) and connect them to get the dilated triangle.