A geometric shape on a coordinate grid has a vertex at T(2, -5). The shape is translated 3… — ACT

A geometric shape on a coordinate grid has a vertex at $T(2, -5)$ . The shape is translated $3$ units to the left and $4$ units up, and then the resulting image is reflected across the $y$ -axis. What are the coordinates of the final image of vertex $T$ ?

A
$(-5, -1)$
B
$(-6, -8)$
$(1, -1)$ Answer
D
$(1, -9)$
E
$(-5, -9)$

Answer

The correct coordinates of the final image of vertex

T

are

(1, -1)

To find the coordinates of the final image, we apply the transformations in the specified order. First, translating the point

(2, -5)

3

units to the left subtracts

3

from the

x

-coordinate, and translating it

4

units up adds

4

to the

y

-coordinate:

(2 - 3, -5 + 4) = (-1, -1)

. Second, reflecting the point

(-1, -1)

across the

y

-axis negates the

x

-coordinate while keeping the

y

-coordinate the same:

(-(-1), -1) = (1, -1)

Step-by-Step Solution

Apply the horizontal and vertical translations to the pre-image point

T(2, -5)

Translating

3

units left subtracts

3

from the

x

-coordinate (

2 - 3 = -1

). Translating

4

units up adds

4

to the

y

-coordinate (

-5 + 4 = -1

). The intermediate point is

(-1, -1)

A translation of

h

units horizontally and

k

units vertically maps

(x, y)

(x + h, y + k)

Reflect the intermediate point

(-1, -1)

across the

y

-axis.

Reflecting across the

y

-axis negates the

x

-coordinate while keeping the

y

-coordinate the same:

(-(-1), -1) = (1, -1)

A reflection across the

y

-axis maps any point

(x, y)

(-x, y)

Key Concept

Transformations in the Coordinate Plane

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic