Question

1. triangle pqr is shown.

what are the coordinates of ( p ) when ( \triangle pqr ) is dilated by a scale factor of 3 using the origin as the center?
a. ( (6,18) ) b. ( left(3,\frac{2}{3}
ight) ) c. ( left(\frac{2}{3},3
ight) ) d. ( (18,6) )

Explanation:

Step1: Apply the dilation formula

When a point \((x,y)\) is dilated by a scale factor \(k\) with the origin \((0,0)\) as the center of dilation, the formula for the new coordinates \((x',y')\) is \(x' = kx\) and \(y'=ky\). Here, the point \(P\) has coordinates \((6,2)\) and the scale factor \(k = 3\).

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

For the \(x\) - coordinate of \(P'\), use \(x'=kx\). Substitute \(x = 6\) and \(k = 3\), so \(x'=3\times6=18\).

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

For the \(y\) - coordinate of \(P'\), use \(y'=ky\). Substitute \(y = 2\) and \(k = 3\), so \(y'=3\times2 = 6\).

Answer:

D. \((18,6)\)