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Difficulty: EasyTransformations in the Coordinate Plane

A scientist maps the movement of a cell on a coordinate grid. The cell is initially located at the point (2,−5)(2, -5). The cell then moves to a new position after being translated 6 units to the left and 4 units up. What are the coordinates of the cell's new position?

  1. A
    (−4,−9)(-4, -9)
  2. B
    (8,−1)(8, -1)
  3. (−4,−1)(-4, -1)Answer
  4. D
    (8,−9)(8, -9)
  5. E
    (−1,−4)(-1, -4)

Answer

The correct position of the cell is (−4,−1)(-4, -1).
To find the coordinates of the new position, apply the translation to the initial coordinates (2,−5)(2, -5). A translation of 6 units to the left subtracts 6 from the x-coordinate: 2−6=−42 - 6 = -4. A translation of 4 units up adds 4 to the y-coordinate: −5+4=−1-5 + 4 = -1. This results in the coordinates (−4,−1)(-4, -1).

Step-by-Step Solution

1
Calculate the new x-coordinate by applying the horizontal translation.
The initial x-coordinate is 22. Translating 6 units to the left means subtracting 6: 2−6=−42 - 6 = -4.
A horizontal shift to the left decreases the x-coordinate value.
2
Calculate the new y-coordinate by applying the vertical translation.
The initial y-coordinate is −5-5. Translating 4 units up means adding 4: −5+4=−1-5 + 4 = -1.
A vertical shift upward increases the y-coordinate value.
3
Combine the new coordinates into an ordered pair (x,y)(x, y).
The new coordinates are (−4,−1)(-4, -1).
The coordinates are represented by the new horizontal position followed by the new vertical position.

Key Concept

Translating a point in the coordinate plane by modifying its coordinates: (x,y)→(x+h,y+k)(x, y) \rightarrow (x + h, y + k), where hh is the horizontal shift and kk is the vertical shift.
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Topics

Transformations in the Coordinate Plane

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