In the standard (x,y) coordinate plane, the point A(-4, 3) is reflected across the x-axis … — ACT

In the standard $(x,y)$ coordinate plane, the point $A(-4, 3)$ is reflected across the $x$ -axis and then translated $5$ units to the right to map onto point $A'$ . What are the coordinates of $A'$ ?

$(1, -3)$ Answer
B
$(-9, -3)$
C
$(1, 3)$
D
$(9, 3)$
E
$(-9, 3)$

Answer

(1, -3)

Reflecting the point

A(-4, 3)

across the

x

-axis negates its

y

-coordinate, resulting in

(-4, -3)

. Then, translating this point

5

units to the right increases its

x

-coordinate by

5

, which yields

(-4 + 5, -3) = (1, -3)

Step-by-Step Solution

Reflect the point

A(-4, 3)

across the

x

-axis.

The rule for reflection across the

x

-axis is

(x, y) \rightarrow (x, -y)

. Applying this rule to

A(-4, 3)

yields the intermediate point

(-4, -3)

A reflection across the

x

-axis negates the

y

-coordinate of the point while keeping the

x

-coordinate the same.

Translate the reflected point

(-4, -3)

5

units to the right.

The rule for translating a point

h

units to the right is

(x, y) \rightarrow (x + h, y)

. Adding

5

to the

x

-coordinate yields

(-4 + 5, -3) = (1, -3)

Translating a point to the right increases its

x

-coordinate by the translation distance.

Key Concept

Applying a sequence of coordinate transformations (reflection followed by translation) to a point.

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

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