Question

triangle def has coordinates ( d(4,-1) ), ( e(5,2) ), and ( f(1,2) ). determine the coordinates of the vertices of the image after a reflection in the y - axis.

( \bigcirc ) a) ( d(4,1) ), ( e(5,-2) ), and ( f(1,-2) )

( \bigcirc ) b) ( d(5,-1) ), ( e(6,2) ), and ( f(2,2) )

( \bigcirc ) c) ( d(-4,-1) ), ( e(-5,2) ), and ( f(-1,2) )

( \bigcirc ) d) ( d(1,0) ), ( e(2,3) ), and ( f(-2,3) )

need help?

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 point \(D(4, - 1)\)

For point \(D(4,-1)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = 4\) and \(y=-1\). So \(D(4,-1)\to D'(-4,-1)\)

Step3: Apply the rule to point \(E(5,2)\)

For point \(E(5,2)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = 5\) and \(y = 2\). So \(E(5,2)\to E'(-5,2)\)

Step4: Apply the rule to point \(F(1,2)\)

For point \(F(1,2)\), using the rule \((x,y)\to(-x,y)\), we substitute \(x = 1\) and \(y = 2\). So \(F(1,2)\to F'(-1,2)\)

Answer:

C. \(D'(-4,-1)\), \(E'(-5,2)\), and \(F'(-1,2)\)