Answer:
Distance = 5 units
Step-by-step explanation:
The given problem asks us to determine the distance between two points, (1, 5) and (5, 2).
Solution:
In order to find the distance between two points, we can use the following distance formula:
[tex]\displaystyle\mathsf{Distance\:(D)= \sqrt{(x_2\:-x_1)^2\:+\:(y_2\:-y_1)^2}}[/tex]
Let (x₁, y₁) = (1, 5)
(x₂, y₂) = (5, 2)
Step 1: Substitute points into the formula:
[tex]\displaystyle\mathsf{Distance\:(D)= \sqrt{(x_2\:-x_1)^2\:+\:(y_2\:-y_1)^2}}[/tex]
[tex]\displaystyle\mathsf{Distance\:(D)= \sqrt{(5\:-1)^2\:+\:(2\:-5)^2}}[/tex]
Step 2: Subtract the integers in each of the parenthesis under the radical:
[tex]\displaystyle\mathsf{Distance\:(D)= \sqrt{(4)^2\:+\:(-3)^2}}[/tex]
Step 3: Evaluate the powers (exponents):
[tex]\displaystyle\mathsf{Distance\:(D)= \sqrt{16\:+\:9}}[/tex]
Step 4: Add 16 and 9:
[tex]\displaystyle\mathsf{Distance\:(D)= \sqrt{25}}[/tex]
Step 5: Take the square root of 25:
⇒ Distance (D) = 5 units.
Final Answer:
Therefore, the distance between points (1, 5) and (5, 2) is 5 units.
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Keywords:
Distance formula
Two points
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