Question

Triangle ABC
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

To find the new coordinates of the points \( A', B', \) and \( C' \) after reflecting triangle ABC across the x-axis, we need to understand how reflection across the x-axis works:

When a point \((x, y)\) is reflected across the x-axis, its coordinates change to \((x, -y)\).

Given the original points:
- \( A(-4, -1) \)
- \( B(-5, -2) \)
- \( C(-10, -1) \)

Now we reflect each point:

1. For point \( A(-4, -1) \):
\[
A' = (-4, -(-1)) = (-4, 1)
\]

2. For point \( B(-5, -2) \):
\[
B' = (-5, -(-2)) = (-5, 2)
\]

3. For point \( C(-10, -1) \):
\[
C' = (-10, -(-1)) = (-10, 1)
\]

Thus, the coordinates of the reflected points are:
- \( A'(-4, 1) \)
- \( B'(-5, 2) \)
- \( C'(-10, 1) \)

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