Question

δeag has vertices e(1,5), a(3,4), and g(2,2). answer parts a and b.
a. what graph shows δeag and its image after a reflection across the line x = -1? choose the correct graph below
○ a.
graph a
○ b.
graph b
○ c.
graph c
○ d.
graph d

Explanation:

Step1: Recall reflection formula

To reflect a point \((x,y)\) across the line \(x = a\), the new \(x\)-coordinate is \(x'=2a - x\), and \(y\)-coordinate remains \(y\). Here, \(a=-1\), so the formula for reflection across \(x = - 1\) is \(x'=2\times(-1)-x=-2 - x\), \(y' = y\).

Step2: Find reflected points

• For point \(E(1,5)\):

\(x'=-2 - 1=-3\), \(y' = 5\), so \(E'(-3,5)\)

• For point \(A(3,4)\):

\(x'=-2 - 3=-5\), \(y' = 4\), so \(A'(-5,4)\)

• For point \(G(2,2)\):

\(x'=-2 - 2=-4\), \(y' = 2\), so \(G'(-4,2)\)

Now, we check the graphs:

• In option A: The coordinates of the reflected triangle do not match our calculated points.
• In option B: The coordinates of the reflected triangle ( \(E'(-3,5)\), \(A'(-5,4)\), \(G'(-4,2)\)) match the blue triangle's coordinates.
• In option C: The coordinates of the reflected triangle do not match our calculated points.
• In option D: The coordinates of the reflected triangle do not match our calculated points.

Answer:

B