Question

point q (5, -3) is dilated with a scale factor of 2 and the center of dilation at the origin. what are the coordinates of q? (2.5, -1.5) (5, -6) (0, 0) (10, -6)

Explanation:

Step1: Apply the dilation formula

When a point \((x,y)\) is dilated with a scale factor \(k\) and center of dilation at the origin \((0,0)\), the formula for the new coordinates \((x',y')\) is \(x' = kx\) and \(y'=ky\). Here \(x = 5\), \(y=-3\) and \(k = 2\).

Step2: Calculate the new \(x\) - coordinate

Substitute \(x = 5\) and \(k = 2\) into \(x'=kx\). So \(x'=2\times5=10\).

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

Substitute \(y=-3\) and \(k = 2\) into \(y'=ky\). So \(y'=2\times(-3)=-6\).

Answer:

\((10,-6)\)