Question

1. draw the dilation for triangle pqr with a scale factor of 4 using point r as the center of dilation.

Explanation:

Step1: Recall dilation formula

For a dilation with center \((x_0,y_0)\) and scale - factor \(k\), the new coordinates \((x',y')\) of a point \((x,y)\) are given by \((x',y')=(x_0 + k(x - x_0),y_0 + k(y - y_0))\). Here, the center of dilation \(R=(1,1)\) and \(k = 4\).

Step2: Find new coordinates of point P

Let \(P=(1,3)\). Using the dilation formula: \(x_0 = 1,y_0 = 1,x = 1,y = 3,k = 4\).
\(x'=1+4\times(1 - 1)=1\)
\(y'=1+4\times(3 - 1)=1 + 8=9\). So the new point \(P'\) is \((1,9)\).

Step3: Find new coordinates of point Q

Let \(Q=(3,1)\). Using the dilation formula: \(x_0 = 1,y_0 = 1,x = 3,y = 1,k = 4\).
\(x'=1+4\times(3 - 1)=1+8 = 9\)
\(y'=1+4\times(1 - 1)=1\). So the new point \(Q'\) is \((9,1)\).

Step4: Draw the new triangle

Plot the points \(P'(1,9)\), \(Q'(9,1)\) and \(R(1,1)\) and connect them to form the dilated triangle \(P'Q'R\).

Answer:

Plot the points \(P'(1,9)\), \(Q'(9,1)\) and \(R(1,1)\) and connect them to get the dilated triangle of \(\triangle PQR\) with a scale - factor of 4 and center of dilation at \(R\).