In the standard (x,y) coordinate plane, point P has coordinates (3, 2). If point P is refl… — ACT

In the standard $(x,y)$ coordinate plane, point $P$ has coordinates $(3, 2)$ . If point $P$ is reflected across the $y$ -axis and then translated $4$ units up to create point $P'$ , what are the coordinates of $P'$ ?

$(-3, 6)$ Answer
B
$(-3, 2)$
C
$(-3, -2)$
D
$(1, 2)$
E
$(3, 2)$

Answer

The coordinates

(-3, 6)

Reflecting the point

(3, 2)

across the

y

-axis changes the sign of the

x

-coordinate, producing

(-3, 2)

. Translating this resulting point

4

units up adds

4

to the

y

-coordinate, giving the final coordinates

(-3, 6)

Step-by-Step Solution

Reflect the point

P(3, 2)

across the

y

-axis.

The

x

-coordinate changes sign, while the

y

-coordinate remains unchanged, yielding

(-3, 2)

A reflection across the

y

-axis maps any point

(x, y)

(-x, y)

Translate the point

(-3, 2)

up by

4

units.

Add

4

to the

y

-coordinate:

2 + 4 = 6

, yielding

(-3, 6)

A translation of

d

units upward maps any point

(x, y)

(x, y + d)

Key Concept

Applying a sequence of transformations to a point in the coordinate plane by first reflecting it across an axis and then translating it.

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