Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

1. First, identify the original coordinates of the vertices:

• From the graph, the coordinates of point \(L\) are \((- 2,-1)\), the coordinates of point \(M\) are \((-1,2)\), and the coordinates of point \(N\) are \((0, - 2)\).

1. Recall the rule for dilation centered at the origin:

• If a point \((x,y)\) is dilated with a scale - factor \(k\) centered at the origin, the new coordinates \((x',y')\) are given by the formula \((x',y')=(k\cdot x,k\cdot y)\). Here, \(k = 4\).

1. Calculate the new coordinates of point \(L\):

• For point \(L(-2,-1)\), using the dilation formula \((x',y')=(k\cdot x,k\cdot y)\) with \(k = 4\), we have \(x'=4\times(-2)=-8\) and \(y'=4\times(-1)=-4\). So the new coordinates of \(L\) are \((-8,-4)\).

1. Calculate the new coordinates of point \(M\):

• For point \(M(-1,2)\), \(x'=4\times(-1)=-4\) and \(y'=4\times2 = 8\). So the new coordinates of \(M\) are \((-4,8)\).

1. Calculate the new coordinates of point \(N\):

• For point \(N(0,-2)\), \(x'=4\times0 = 0\) and \(y'=4\times(-2)=-8\). So the new coordinates of \(N\) are \((0,-8)\).

Answer:

The coordinates of \(L\) after dilation are \((-8,-4)\), the coordinates of \(M\) after dilation are \((-4,8)\), and the coordinates of \(N\) after dilation are \((0,-8)\).