Question

the vertices of △def are located at d(3, -2), e(4, 3), and f(-3, 4). △def is reflected across the y - axis to form △def.
what are the coordinates of △def?
complete the statements by selecting the correct choice.
the vertices of △def are d, e, and f.
d: (-3, 2), (-3, -2), (3, 2), (-2, 3)
e: (-4, 3), (-4, -3), (4, -3), (3, 4)
f: (3, 4), (3, -4), (-3, -4), (4, -3)

Explanation:

Step1: Recall the reflection rule

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

Step2: Apply the rule to each vertex

• For vertex \(D(3, - 2)\):

Using the rule \((x,y)\to(-x,y)\), we substitute \(x = 3\) and \(y=-2\). So \(D(3,-2)\to D'(-3,-2)\).

• For vertex \(E(4,3)\):

Substitute \(x = 4\) and \(y = 3\) into the rule \((x,y)\to(-x,y)\). Then \(E(4,3)\to E'(-4,3)\).

• For vertex \(F(-3,4)\):

Substitute \(x=-3\) and \(y = 4\) into the rule \((x,y)\to(-x,y)\). We get \(F(-3,4)\to F'(3,4)\).

Answer:

\(D'\): \((-3,-2)\), \(E'\): \((-4,3)\), \(F'\): \((3,4)\)