2) If you are given two points in space, P1 (X1,yı) and P2 (X2,yz), demonstrate why the distance between the two points can be represented by the following formula: d = (x2 - x1)? + (y2 - Y1)2
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
![**Distance Formula Explanation**
Given two points in space, \( P_1 (x_1, y_1) \) and \( P_2 (x_2, y_2) \), we can calculate the distance between these two points using the distance formula derived from the Pythagorean theorem. This formula is represented as:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
This formula is applicable in a Cartesian coordinate system, allowing us to find the straight-line distance \( d \) between any two points \( P_1 \) and \( P_2 \).
**Explanation:**
1. **Horizontal Distance:** Calculate the difference in the x-coordinates, \( x_2 - x_1 \).
2. **Vertical Distance:** Calculate the difference in the y-coordinates, \( y_2 - y_1 \).
3. **Square of Differences:** Square each of the differences.
4. **Sum of Squares:** Add the squared differences.
5. **Square Root:** Take the square root of the sum to find the distance \( d \).
This formula essentially combines the changes in horizontal and vertical distances to provide the direct path between the two points in a two-dimensional plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8ea8be2a-b1da-472d-bbc4-91d8ae774356%2F1c7beac6-a0ed-4912-ae47-a5ba3382bff9%2Fm4bw4bk_processed.jpeg&w=3840&q=75)
Step by step
Solved in 2 steps with 1 images
