A triangle has a vertex located at the point with coordinates (7, -2). If the triangle is … — ACT

A triangle has a vertex located at the point with coordinates $(7, -2)$ . If the triangle is translated $4$ units to the left and $5$ units up, what are the coordinates of this vertex after the translation?

$(3, 3)$ Answer
B
$(11, 3)$
C
$(3, -7)$
D
$(11, -7)$
E
$(-6, 12)$

Answer

(3, 3)

Applying a translation of

4

units left means subtracting

4

from the

x

-coordinate of the point

(7, -2)

, resulting in

7 - 4 = 3

. Translating

5

units up means adding

5

to the

y

-coordinate, resulting in

-2 + 5 = 3

. Therefore, the new coordinates of the vertex are

(3, 3)

Step-by-Step Solution

Identify the horizontal translation and apply it to the

x

-coordinate.

Since the translation is

4

units to the left, we subtract

4

from the initial

x

-coordinate of

7

7 - 4 = 3

Moving left along the

x

-axis decreases the coordinate value.

Identify the vertical translation and apply it to the

y

-coordinate.

Since the translation is

5

units up, we add

5

to the initial

y

-coordinate of

-2

-2 + 5 = 3

Moving up along the

y

-axis increases the coordinate value.

Combine the new coordinates into an ordered pair.

The final coordinates are

(3, 3)

The coordinates

(x', y')

form the final position of the vertex.

Key Concept

Translating points in the coordinate plane by adding or subtracting values from their coordinates.

Estimated Time:45s

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