Question

a dilation with a scale factor of 1/5 and centered at the origin is applied to mn with endpoints m(-2, -4) and n(1, 5). drag and drop to match the correct coordinates with the point. coordinates of m coordinates of n (-2/5, -4/5) (-2/5, -4) (1, 1) (1/5, 1) (-10, -20) (-10, -4) (5, 5)

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if a point \((x,y)\) is dilated, the new point \((x',y')\) has coordinates \((kx,ky)\). Here \(k = \frac{1}{5}\).

Step2: Find coordinates of \(M'\)

Given \(M(-2,-4)\), then \(x=-2\), \(y = - 4\), and \(k=\frac{1}{5}\). So \(x'=k\times x=\frac{1}{5}\times(-2)=-\frac{2}{5}\) and \(y'=k\times y=\frac{1}{5}\times(-4)=-\frac{4}{5}\). The coordinates of \(M'\) are \((-\frac{2}{5},-\frac{4}{5})\).

Step3: Find coordinates of \(N'\)

Given \(N(1,5)\), then \(x = 1\), \(y = 5\), and \(k=\frac{1}{5}\). So \(x'=k\times x=\frac{1}{5}\times1=\frac{1}{5}\) and \(y'=k\times y=\frac{1}{5}\times5 = 1\). The coordinates of \(N'\) are \((\frac{1}{5},1)\).

Answer:

Coordinates of \(M'\): \((-\frac{2}{5},-\frac{4}{5})\)
Coordinates of \(N'\): \((\frac{1}{5},1)\)