A drone's position on a coordinate grid is represented by the point (3, -5). If the drone … — ACT

A drone's position on a coordinate grid is represented by the point $(3, -5)$ . If the drone undergoes a translation of $4$ units to the left and $2$ units up, what are the coordinates of its new position on the grid?

A
$(7, -7)$
B
$(-1, -7)$
C
$(7, -3)$
D
$(1, -1)$
$(-1, -3)$ Answer

Answer

(-1, -3)

The correct answer is

(-1, -3)

. A horizontal translation of

4

units left subtracts

4

from the original

x

-coordinate of

3

, resulting in a new

x

-coordinate of

3 - 4 = -1

. A vertical translation of

2

units up adds

2

to the original

y

-coordinate of

-5

, resulting in a new

y

-coordinate of

-5 + 2 = -3

. This places the drone at

(-1, -3)

Step-by-Step Solution

Calculate the new x-coordinate

x' = 3 - 4 = -1

Translating

4

units to the left means subtracting

4

from the initial

x

-coordinate of

3

Calculate the new y-coordinate

y' = -5 + 2 = -3

Translating

2

units up means adding

2

to the initial

y

-coordinate of

-5

Combine the new coordinates to write the final position

(-1, -3)

Combining the calculated

x

-coordinate and

y

-coordinate yields the final position of the drone.

Key Concept

Performing translations in the coordinate plane

Estimated Time:45s

Question

Answer

Step-by-Step Solution

Key Concept

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