Question

If the point (2,5) is shifted 3 units to the right and 2 units down, what are its new coordinates?

Short answer

The new coordinates are (5,3).

Step-by-step solution

Identify Initial Coordinates

The initial coordinates of the point are given as (2,5), where 2 is the x-coordinate and 5 is the y-coordinate.

Shift Point 3 Units to the Right

To shift the point 3 units to the right, add 3 to the x-coordinate. The x-coordinate changes from 2 to 2+3=5.

Shift Point 2 Units Down

To shift the point 2 units down, subtract 2 from the y-coordinate. The y-coordinate changes from 5 to 5-2=3.

Write New Coordinates

After performing the shifts, the new coordinates of the point are (5,3).

Key concepts

Point Translation Explanation

In coordinate geometry, the concept of point translation is crucial. It involves moving a point from one location to another without changing its orientation or size. To translate a point, you simply add or subtract values from its coordinates.

For instance, if you have a point (2,5) and you want to move it, you follow these steps:

• Identify how much to move the point along the x-axis (left or right)
• Identify how much to move the point along the y-axis (up or down)

In our exercise, we shifted the point 3 units to the right and 2 units down. This kind of translation is systematic and straightforward once you understand how to adjust the coordinates.

Understanding the X-Coordinate

The x-coordinate represents the horizontal position of a point on the Cartesian plane. It's the first number in an ordered pair, like (2,5).

When shifting a point horizontally:

• To move the point right, you add to the x-coordinate
• To move the point left, you subtract from the x-coordinate

In our exercise, the initial x-coordinate was 2. We shifted it 3 units to the right, transforming the x-coordinate from 2 to 5. This change illustrates how the x-coordinate influences the point's location along the horizontal axis.

Understanding the Y-Coordinate

The y-coordinate shows the vertical position of a point on the Cartesian plane. It’s the second number in an ordered pair, like (2,5).

When shifting a point vertically:

• To move the point up, you add to the y-coordinate
• To move the point down, you subtract from the y-coordinate

In our exercise, the initial y-coordinate was 5. To shift the point 2 units down, we subtracted 2 from the y-coordinate, changing it from 5 to 3. This example clearly demonstrates how moving up or down affects the y-coordinate of a point.