In the xy-plane, point P has coordinates (3, -4). Point P is reflected across the y-axis t… — GRE General Test

In the $xy$ -plane, point $P$ has coordinates $(3, -4)$ . Point $P$ is reflected across the $y$ -axis to form point $Q$ . Point $Q$ is then translated upward by $2$ units to form point $R$ . Which of the following statements must be true? Select all that apply.

The coordinates of point $Q$ are $(-3, -4)$ .Answer
Point $R$ lies in Quadrant III.Answer
C
The distance between point $P$ and point $Q$ is $8$ units.
D
The $y$ -coordinate of point $R$ is $2$ .

Answer

The correct statements are that the coordinates of point

Q

are

(-3, -4)

and that point

R

lies in Quadrant III.

Reflecting

(3, -4)

across the

y

-axis yields

(-3, -4)

for point

Q

. Translating

(-3, -4)

upward by

2

units gives

(-3, -2)

for point

R

. Because both coordinates of

R

are negative, it resides in Quadrant III.

Step-by-Step Solution

Perform the reflection across the

y

-axis

Point

Q = (-3, -4)

Reflecting across the

y

-axis negates the

x

-coordinate while keeping the

y

-coordinate the same.

Perform the vertical translation upward by

2

units

Point

R = (-3, -4 + 2) = (-3, -2)

Translating upward adds

2

to the

y

-coordinate of point

Q

Determine the quadrant of point

R

Quadrant III

Points with

x < 0

and

y < 0

are located in Quadrant III.

Calculate the distance between point

P(3, -4)

and point

Q(-3, -4)

Distance =

|3 - (-3)| = 6

units

Points

P

and

Q

lie on the horizontal line

y = -4

, so the distance is the difference in their

x

-coordinates.

Key Concept

Coordinate transformations including axis reflections and translations in the Cartesian plane

Question

Answer

Step-by-Step Solution

Key Concept

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