Find the distance between the pair of points. (6,9) and (12,17) The distance between the points is units. (Round to two decimal places as needed.)
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.
![**Finding the Distance Between Two Points**
To determine the distance between the pair of points \((6, 9) \) and \((12, 17) \):
1. **Identify the coordinates**:
\[
(x_1, y_1) = (6, 9)
\]
\[
(x_2, y_2) = (12, 17)
\]
2. **Apply the distance formula**: The distance \(d\) between two points \((x_1, y_1) \) and \((x_2, y_2) \) is given by:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]
3. **Substitute the coordinates** into the formula:
\[
d = \sqrt{(12 - 6)^2 + (17 - 9)^2}
\]
\[
d = \sqrt{6^2 + 8^2}
\]
\[
d = \sqrt{36 + 64}
\]
\[
d = \sqrt{100}
\]
\[
d = 10
\]
Thus, the distance between the points is 10 units. Round to two decimal places as needed, though in this case, the exact answer is already 10.00 units.
**Visualization**:
Imagining this on a coordinate plane, the two points create a right triangle with legs of length 6 and 8 units. The distance calculated is the length of the hypotenuse of this triangle, which confirms our calculations using the Pythagorean Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1366b624-6ac4-48df-86a5-7d6d7519d7d6%2F1ae2c225-9352-4838-aa5a-1e0cdd1132e8%2Fami07el_processed.jpeg&w=3840&q=75)
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