Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are \(F(- 5,5)\), \(G(4,5)\), \(H(-5,-4)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 2\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \(x'=k\times x\) and \(y'=k\times y\).
For point \(F(-5,5)\):
\(x_F'=2\times(-5)=-10\), \(y_F'=2\times5 = 10\), so the new coordinates of \(F\) are \((-10,10)\).
For point \(G(4,5)\):
\(x_G'=2\times4 = 8\), \(y_G'=2\times5=10\), so the new coordinates of \(G\) are \((8,10)\).
For point \(H(-5,-4)\):
\(x_H'=2\times(-5)=-10\), \(y_H'=2\times(-4)=-8\), so the new coordinates of \(H\) are \((-10,-8)\).

Answer:

The new coordinates of \(F\) are \((-10,10)\), of \(G\) are \((8,10)\) and of \(H\) are \((-10,-8)\)