Rounding the Result: What is the Distance between Points F(2, 9) and G(4, 14)? Round to the Nearest Whole Number.

What is the Distance between Points F(2, 9) and G(4, 14)? Round to the Nearest Whole Number.

I’ll calculate the distance between points f(2, 9) and g(4, 14) for you. To find the distance between two points in a coordinate plane, we can use the distance formula. The formula is given by:

distance = √((x2 – x1)^2 + (y2 – y1)^2)

By substituting the values of f(2, 9) and g(4, 14) into the formula, we get:

distance = √((4 – 2)^2 + (14 – 9)^2) = √((2^2) + (5^2)) = √(4 + 25) = √29

Rounding to the nearest whole number, the distance between points f(2, 9) and g(4, 14) is approximately 5 units.

Calculating distances between points in a coordinate plane can help us understand spatial relationships and solve various mathematical problems. In this case, we’ve determined that the distance between f(2, 9) and g(4, 14) is approximately 5 units.

Calculating the Distance Between Two Points

When it comes to finding the distance between two points in a coordinate plane, we can rely on a powerful tool called the distance formula. This formula allows us to calculate the straight-line distance between any two points, regardless of their position. It’s an essential concept in geometry and is often employed in various real-life scenarios.

The distance formula states that the distance (d) between two points, let’s call them point A(x1, y1) and point B(x2, y2), can be determined using the following equation:

d = √((x2 – x1)^2 + (y2 – y1)^2)

Applying the Formula to Points f(2, 9) and g(4, 14)

Let’s put this formula into action by calculating the distance between points f(2, 9) and g(4, 14). Considering that our x-coordinates are 2 and 4 respectively, while our y-coordinates are 9 and 14 respectively, we can substitute these values into our formula:

d = √((4 – 2)^2 + (14 – 9)^2)

Simplifying further:

d = √(2^2 + 5^2)

= √(4 + 25)

= √29

Thus, we find that the exact distance between points f(2,9) and g(4,14) is √29 units.

Rounding the Result to the Nearest Whole Number

To round this result to the nearest whole number as specified in your question (“round to the nearest whole number”), we need to determine whether √29 is closer to either its floor or ceiling value. In this case:

• The floor value of √29 is 5, as √29 is greater than 5 but less than 6.
• The ceiling value of √29 is 6, as √29 is closer to 6 than it is to 5.

Therefore, rounding √29 to the nearest whole number yields a distance of 6 units between points f(2,9) and g(4,14).

By utilizing the distance formula and rounding the result appropriately, we have successfully calculated the distance between these two points. This process can be applied to any pair of coordinates in a similar manner.

Understanding the Coordinates of Point F

In this section, let’s delve into the coordinates of point F and gain a better understanding of its significance in calculating the distance between points F(2, 9) and G(4, 14).

Now turning our attention specifically to point F(2, 9), we can break down its coordinates. The x-coordinate is 2 and denotes that it lies 2 units along the x-axis from the origin. Similarly, for the y-coordinate of 9, it indicates that point F is positioned 9 units up from the origin on the y-axis.

By interpreting these coordinates accurately, we establish a foundation for finding distances between points. In our case, we want to determine how far apart point F(2, 9) is from point G(4, 14).

To calculate this distance accurately using Euclidean geometry principles (also known as straight-line distance or Pythagorean theorem), we need to apply a simple formula:

Distance = √((x2 – x1)^2 + (y2 – y1)^2)

Applying this formula specifically to our scenario:

Distance = √((4-2)^2 + (14-9)^2)

Simplifying further:

Distance = √((2^2) + (5^2))

Calculating this equation gives us:

Distance ≈ √(4 + 25) ≈ √29

Finally rounding to nearest whole number:

Distance ≈ 5

Hence, after rounding to the nearest whole number, the distance between points F(2, 9) and G(4, 14) is approximately 5 units.