Question

1. the table below shows the coordinates of triangle pqr

part a
fill in the table above for the coordinates of ( p ^ { prime } ), ( q ^ { prime } ), and ( r ^ { prime } ) after a
reflection over the y-axis.

1. describe a reflection that would move shape 1 to match shape 2.

1. point ( a ( 3,6 ) ) is rotated ( 270 ^ { circ } ) counterclockwise about the origin. what is the coordinate of ( a ^ { prime } ) ? circle

the best answer.
(a) ( ( - 6,3 ) )
(c) ( ( 6 , - 3 ) )
(b) ( ( 3,6 ) )
(d) ( ( - 3 , - 6 ) )

Explanation:

Part 4

Step1: Recall the rule for reflection over the \(y -\)axis

When a point \((x,y)\) is reflected over the \(y -\)axis, the rule is \((x,y)\to(-x,y)\).

Step2: Apply the rule to point \(P(-3,2)\)

For \(P(-3,2)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x=-3\) and \(y = 2\). Then \(x'=-(-3)=3\) and \(y' = 2\), so \(P'=(3,2)\).

Step3: Apply the rule to point \(Q(-3,6)\)

For \(Q(-3,6)\), substitute \(x=-3\) and \(y = 6\) into the rule \((x,y)\to(-x,y)\). Then \(x'=-(-3)=3\) and \(y' = 6\), so \(Q'=(3,6)\).

Step4: Apply the rule to point \(R(-2,7)\)

For \(R(-2,7)\), substitute \(x=-2\) and \(y = 7\) into the rule \((x,y)\to(-x,y)\). Then \(x'=-(-2)=2\) and \(y' = 7\), so \(R'=(2,7)\).

Part 5

Step1: Analyze the position of the shapes

The \(x -\)coordinates of the corresponding points of shape 1 and shape 2 are opposite in sign.
Using the reflection rule \((x,y)\to(-x,y)\) (reflection over the \(y -\)axis). Since the \(y -\)coordinates of corresponding points of the two shapes are the same and the \(x -\)coordinates are opposite in sign, the reflection is over the \(y -\)axis.

Part 6

Step1: Recall the rotation rule for \(270^{\circ}\) counter - clockwise about the origin

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y,-x)\).

Step2: Apply the rule to point \(A(3,6)\)

For \(A(3,6)\), substitute \(x = 3\) and \(y=6\) into the rule \((x,y)\to(y,-x)\). We get \(x'=6\) and \(y'=-3\). So the coordinates of \(A'\) are \((6,-3)\).

Answer:

• Part 4: \(P'=(3,2)\), \(Q'=(3,6)\), \(R'=(2,7)\)
• Part 5: Reflection over the \(y -\)axis
• Part 6: (c) \((6,-3)\)