Question

A triangle has vertices (1, 4), (1, 1), and (−3, 1). The triangle is dilated by a scale factor of 2, thentranslated 5 units up, and then rotated 90° counterclockwise about the origin. What are the vertices of the image of the triangle?

Answer 1

`\begin{gathered} A=(-13,2) \\ B=(-7,2) \\ C=(-7,-6) \end{gathered}`

Step-by-step explanation

Given;

`\begin{gathered} A=(1,4) \\ B=(1,1) \\ C=(-3,1) \end{gathered}`

Dilate means (multiply each coordinate by 2);

`\begin{gathered} A=(2,8) \\ B=(2,2) \\ C=(-6,2) \end{gathered}`

Translate 5 unit up means (y-axis will increase by 5 units);

hence;

`\begin{gathered} A=(2,8+5)=(2,13) \\ B=(2,2+5)=(2,7) \\ C=(-6,2+5)=(-6,7) \end{gathered}`

Rotate 90 means (x,y) becomes (-y,x) (counterclockwise) ;

`\begin{gathered} A=(-13,2) \\ B=(-7,2) \\ C=(-7,-6) \end{gathered}`