Question

the coordinates of point l are (4,2). multiply the coordinates by the scale factor, 2. what are the coordinates of point l?

Explanation:

Step1: Recall the dilation formula

When a point \((x,y)\) is dilated by a scale factor \(k\) centered at the origin, the new coordinates \((x',y')\) are given by \((x',y')=(kx,ky)\).

Step2: Identify the values of \(x\), \(y\), and \(k\)

Here, the coordinates of point \(L\) are \((4,2)\), so \(x = 4\), \(y=2\), and the scale factor \(k = 2\).

Step3: Calculate the new \(x\) - coordinate

Using the formula \(x'=kx\), substitute \(k = 2\) and \(x = 4\). Then \(x'=2\times4=8\).

Step4: Calculate the new \(y\) - coordinate

Using the formula \(y'=ky\), substitute \(k = 2\) and \(y = 2\). Then \(y'=2\times2 = 4\).

Answer:

The coordinates of point \(L'\) are \((8,4)\)