Question

a student plots a square on the coordinate plane with vertices at ( a(-2,-2) ), ( b(-2,-7) ), ( c(-7,-7) ) and ( d(-7,-2) ). the student then reflects the square over the ( y )-axis. what are the coordinates of the vertices after the square is reflected over the ( y )-axis?
a. ( a(2,2) ), ( b(7,2) ), ( c(7,7) ), ( d(2,7) )
b. ( a(-2,2) ), ( b(-2,7) ), ( c(-7,7) ), ( d(-7,2) )
c. ( a(2,-2) ), ( b(7,-2) ), ( c(7,-7) ), ( d(2,-7) )
d. ( a(2,-2) ), ( b(2,-7) ), ( c(7,-7) ), ( d(7,-2) )

Explanation:

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 each vertex

• For vertex \(A(-2,-2)\):

Using the rule \((x,y)\to(-x,y)\), we substitute \(x = - 2\) and \(y=-2\). Then \(x\) becomes \(-(-2)=2\), so \(A'=(2,-2)\).

• For vertex \(B(-2,-7)\):

Substitute \(x = - 2\) and \(y = - 7\) into the rule. \(x\) becomes \(-(-2)=2\), so \(B'=(2,-7)\).

• For vertex \(C(-7,-7)\):

Substitute \(x=-7\) and \(y = - 7\) into the rule. \(x\) becomes \(-(-7)=7\), so \(C'=(7,-7)\).

• For vertex \(D(-7,-2)\):

Substitute \(x=-7\) and \(y=-2\) into the rule. \(x\) becomes \(-(-7)=7\), so \(D'=(7,-2)\).

Answer:

D. \(A'(2,-2),B'(2,-7),C'(7,-7),D'(7,-2)\)