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.
a) d(4, 1), e(5, - 2), and f(1, - 2)
b) d(5, - 1), e(6, 2), and f(2, 2)
c) d(- 4, - 1), e(- 5, 2), and f(- 1, 2)
d) d(1, 0), e(2, 3), and f(- 2, 3)

Explanation:

Step1: Recall the reflection rule

When reflecting a point \((x,y)\) 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 get \(D'(-4,-1)\).

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

For point \(E(5,2)\), using the rule \((x,y)\to(-x,y)\), we get \(E'(-5,2)\).

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

For point \(F(1,2)\), using the rule \((x,y)\to(-x,y)\), we get \(F'(-1,2)\).

Answer:

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