Question

challenge the vertices of △abc are a(-2,5), b(-2,4), and c(-5,2). △abc is reflected across the y - axis and then reflected across the x - axis to produce the image △abc. graph △abc and △abc. which graph shows △abc and △abc?

Explanation:

Step1: Find the coordinates after reflection across the y - axis

When a point \((x,y)\) is reflected across the \(y\) - axis, the rule is \((x,y)\to(-x,y)\).
For \(A(-2,5)\), after reflection across the \(y\) - axis, \(A'\) has coordinates \((2,5)\).
For \(B(-2,4)\), after reflection across the \(y\) - axis, \(B'\) has coordinates \((2,4)\).
For \(C(-5,2)\), after reflection across the \(y\) - axis, \(C'\) has coordinates \((5,2)\).

Step2: Find the coordinates after reflection across the x - axis

When a point \((x,y)\) is reflected across the \(x\) - axis, the rule is \((x,y)\to(x, - y)\).
For \(A'(2,5)\), after reflection across the \(x\) - axis, \(A''\) has coordinates \((2,-5)\).
For \(B'(2,4)\), after reflection across the \(x\) - axis, \(B''\) has coordinates \((2,-4)\).
For \(C'(5,2)\), after reflection across the \(x\) - axis, \(C''\) has coordinates \((5,-2)\).

Now, let's analyze the options:

• Option A: The original triangle \(ABC\) has vertices \(A(-2,5)\), \(B(-2,4)\), \(C(-5,2)\) and the reflected triangle \(A''B''C''\) should have vertices \((2,-5)\), \((2,-4)\), \((5,-2)\). This option does not match the correct reflected coordinates.
• Option B: The original triangle \(ABC\) has vertices \(A(-2,5)\), \(B(-2,4)\), \(C(-5,2)\) and the reflected triangle \(A''B''C''\) has vertices \((2,-5)\), \((2,-4)\), \((5,-2)\) which matches the coordinates we found.
• Option C: The coordinates of the reflected triangle do not match the coordinates \((2,-5)\), \((2,-4)\), \((5,-2)\) we calculated.

Answer:

B.