The Right Formula to Find the Distance Between Points P(8, 2) and Q(3, 8) to the Nearest Tenth.

Find the Distance Between Points P(8, 2) and Q(3, 8) to the Nearest Tenth.

Finding the distance between two points on a coordinate plane is a fundamental concept in mathematics. In this article, I’ll show you how to calculate the distance between points P(8, 2) and Q(3, 8) to the nearest tenth. By using a simple formula and applying it step by step, we can determine the precise distance between these two points.

To begin, we’ll utilize the distance formula derived from the Pythagorean theorem. This formula states that the distance between two points (x₁, y₁) and (x₂, y₂) is equal to the square root of [(x₂ – x₁)² + (y₂ – y₁)²]. Applying this formula to our given coordinates of P(8, 2) and Q(3, 8), we can substitute these values into our equation.

By plugging in our values and simplifying through calculations, we’ll arrive at an answer that represents the distance between points P and Q. Rounding this result to the nearest tenth will provide us with a concise measurement.

Join me as we explore this mathematical journey together and discover how to accurately find distances on a coordinate plane. Let’s dive right in!

Understanding the Coordinates of Points P and Q

To find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth, it’s essential to understand how coordinates work. In a two-dimensional Cartesian coordinate system like the one we’re dealing with here, points are represented by an ordered pair (x, y), where x represents the horizontal distance from the origin (typically denoted as “0” on both axes) and y represents the vertical distance.

In our case, point P has coordinates (8, 2), meaning it is located 8 units to the right on the x-axis and 2 units up on the y-axis. Similarly, point Q has coordinates (3, 8), indicating that it is positioned 3 units to the right on the x-axis and 8 units up on the y-axis.

Calculating the Horizontal Distance Between Points P and Q

To determine the horizontal distance between points P and Q, we need to find out how far apart they are in terms of their x-coordinates. In this case, we subtract the smaller x-coordinate from the larger one:

Horizontal Distance = |x₂ – x₁|

Using our example values: Horizontal Distance = |3 – 8| = |-5|

Since distances cannot be negative in this context, we take absolute value: Horizontal Distance = 5

Calculating Vertical Distance Between Points P and Q

Now let’s calculate how far apart points P and Q are vertically. We can do this by finding out their difference in terms of their y-coordinates:

Vertical Distance = |y₂ – y₁|

Plugging in our given values: Vertical Distance = |8 – 2| = |6|

The vertical distance is simply equal to: Vertical Distance = 6

By using these calculations for horizontal and vertical distances between points P and Q, we can then apply the Pythagorean theorem to find the actual distance between them. Stay tuned for the next section where we’ll dive deeper into this topic and explore how to calculate the overall distance accurately! Calculating the Vertical Distance

Now that we have the coordinates of points P(8, 2) and Q(3, 8), let’s calculate the vertical distance between them. The vertical distance represents the difference in their y-coordinates.

To find the vertical distance, we subtract the y-coordinate of point P from the y-coordinate of point Q. In this case, it would be:

Vertical Distance = Qy – Py

Substituting in the given values:

Vertical Distance = 8 – 2 Vertical Distance = 6

The vertical distance between points P(8, 2) and Q(3, 8) is 6 units.

Let’s recap what we’ve done so far:

1. We identified points P and Q with their respective coordinates.
2. We calculated the vertical distance by subtracting Py from Qy.
3. The resulting value gives us the vertical distance between points P and Q.

In our next section, we’ll determine how to calculate the horizontal distance between these two points. Stay tuned!