Question

what are the coordinates of point (2,3) after a translation to the right of 2 units and down 5 units, and then a dilation by a factor of 1.5 about (0,0)? (6, - 3) (0, - 1) (0,2) (3,0)

Explanation:

Step1: Translate the point

For a translation to the right by \(2\) units, add \(2\) to the \(x\) - coordinate. For a translation down by \(5\) units, subtract \(5\) from the \(y\) - coordinate.
If the original point is \((x,y)=(2,3)\), after translation, the new point \((x',y')=(2 + 2,3-5)=(4,-2)\)

Step2: Dilate the translated point

The formula for dilation about the origin \((0,0)\) with a scale factor \(k\) is \((x'',y'')=k(x',y')\). Here \(k = 1.5\) and \((x',y')=(4,-2)\)
\(x''=1.5\times4 = 6\)
\(y''=1.5\times(-2)=-3\)

Answer:

A. \((6,-3)\)