Question

find the image based on the graph of the pre - image. dilation of 1.5 about the origin 23. find r type a response

Explanation:

1. First, assume the coordinates of the vertices of the pre - image triangle:

• Let's assume the coordinates of point \(R\) are \((x_R,y_R)\), point \(S\) are \((x_S,y_S)\), and point \(T\) are \((x_T,y_T)\). From the graph, if we assume \(R(- 2,-2)\), \(S(0,2)\), \(T(2,0)\).
• The rule for a dilation about the origin with a scale factor \(k\) is \((x,y)\to(kx,ky)\). Here, \(k = 1.5\).

1. Calculate the coordinates of the dilated point \(R'\):

• For point \(R(-2,-2)\), using the dilation rule \((x,y)\to(kx,ky)\) with \(k = 1.5\).
• \(x_{R'}=k\times x_R=1.5\times(-2)=-3\).
• \(y_{R'}=k\times y_R=1.5\times(-2)=-3\). So, the coordinates of \(R'\) are \((-3,-3)\).

Step1: Identify dilation rule

The rule for dilation about origin with scale - factor \(k\) is \((x,y)\to(kx,ky)\).

Step2: Apply rule to point \(R\)

Given \(R(-2,-2)\) and \(k = 1.5\), calculate \(x_{R'}=1.5\times(-2)\) and \(y_{R'}=1.5\times(-2)\).

Answer:

\(R'(-3,-3)\)