Question

nia is analyzing a triangle with vertices at ( a(2,1) ), ( b(6,4) ), and ( c(3,7) ). she rotates the triangle ( 90^{circ} ) clockwise around the origin and then translates the image 2 units right and 1 unit up. she wants to understand how these transformations affect the coordinates.
question 4
what is the coordinate rule for a ( 90^{circ} ) clockwise rotation?
( (x,y)
ightarrow(-x,-y) )
( (x,y)
ightarrow(x - h,y + k) )
( (x,y)
ightarrow(y,-x) )
( (x,y)
ightarrow(-y,x) )
question 5
after rotating point ( a(2,1) 90^{circ} ) clockwise, where does it land?
( (3,1) )
( (1,-2) )
( (-2,1) )

Explanation:

Step1: Recall rotation rules

For a \(90^{\circ}\) clockwise rotation about the origin, the rule is \((x,y)\to(y, -x)\).

Step2: Apply the rule to point \(A(2,1)\)

Substitute \(x = 2\) and \(y=1\) into \((x,y)\to(y, -x)\). We get \((1,- 2)\).

Answer:

For question 4: \((x,y)\to(y, -x)\) (the third option).
For question 5: \((1,-2)\) (the second option).