Question

graph the image of (\triangle uvw) after the following sequence of transformations:
rotation (90^{circ}) counterclockwise around the origin
translation 3 units left and 14 units down

Explanation:

Step1: Find coordinates of original triangle

Assume \(U(8,10)\), \(V(4,4)\), \(W(2,10)\)

Step2: Apply rotation \(90^{\circ}\) counter - clockwise

The rule for \(90^{\circ}\) counter - clockwise rotation \((x,y)\to(-y,x)\)

• For \(U(8,10)\): \((- 10,8)\)
• For \(V(4,4)\): \((-4,4)\)
• For \(W(2,10)\): \((-10,2)\)

Step3: Apply translation \(3\) units left and \(14\) units down

The rule for translation \((x,y)\to(x - 3,y-14)\)

• For \(U'(-10,8)\): \((-10-3,8 - 14)=(-13,-6)\)
• For \(V'(-4,4)\): \((-4-3,4-14)=(-7,-10)\)
• For \(W'(-10,2)\): \((-10-3,2-14)=(-13,-12)\)

Answer:

Plot the points \(U''(-13,-6)\), \(V''(-7,-10)\), \(W''(-13,-12)\) and connect them to form the image of \(\triangle UVW\) after the given sequence of transformations.