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 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 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 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

A′(−4,1)
, B′(5,−2)
, and C′(−10,1)

Answer 1

When a point \((x, y)\) is reflected across the x-axis, its y-coordinate changes sign while the x-coordinate remains the same. Therefore, the reflection of point \(A(x, y)\) across the x-axis is given by \(A'(x, -y)\).

Applying this to the coordinates of triangle ABC:

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

   • A' = (-4, -(-1)) = (-4, 1)

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

   • B' = (-5, -(-2)) = (-5, 2)

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

   • C' = (-10, -(-1)) = (-10, 1)

So, the coordinates after the reflection are:

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

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