Triangle ABC

Question

is reflected across the x
-axis. If the coordinates of the original shape are A(−4,−1)
, B(−5,−2)
, and C(−10,−1)
, what are the coordinates of A′
, B′
, and C′
?(1 point)
Responses

A′(−4,1)
, B′(−5,2)
, and C′(−10,1)
upper A prime left parenthesis negative 4 comma 1 right parenthesis , upper B prime left parenthesis negative 5 comma 2 right parenthesis , and upper C prime left parenthesis negative 10 comma 1 right parenthesis

A′(−4,1)
, B′(5,−2)
, and C′(−10,1)
upper A prime left parenthesis negative 4 comma 1 right parenthesis , upper B prime left parenthesis 5 comma negative 2 right parenthesis , and upper C prime left parenthesis negative 10 comma 1 right parenthesis

A′(4,1)
, B′(5,2)
, and C′(10,1)
upper A prime left parenthesis 4 comma 1 right parenthesis , upper B prime left parenthesis 5 comma 2 right parenthesis , and upper C prime left parenthesis 10 comma 1 right parenthesis

A′(4,−1)
, B′(5,−2)
, and C′(10,−1)
upper A prime left parenthesis 4 comma negative 1 right parenthesis , upper B prime left parenthesis 5 comma negative 2 right parenthesis , and upper C prime left parenthesis 10 comma negative 1 right parenthesis

Answer 1

When a point \((x, y)\) is reflected across the x-axis, the new coordinates become \((x, -y)\).

Let's apply this to each of the points A, B, and C:

1. Point A at \((-4, -1)\):

   • Reflection: \((-4, -(-1)) = (-4, 1)\)
   • So, \(A'(-4, 1)\).

2. Point B at \((-5, -2)\):

   • Reflection: \((-5, -(-2)) = (-5, 2)\)
   • So, \(B'(-5, 2)\).

3. Point C at \((-10, -1)\):

   • Reflection: \((-10, -(-1)) = (-10, 1)\)
   • So, \(C'(-10, 1)\).

Now, putting it all together, the coordinates after reflection are:

• \(A'(-4, 1)\)
• \(B'(-5, 2)\)
• \(C'(-10, 1)\)

Thus, the correct response is: A′(−4,1), B′(−5,2), and C′(−10,1).