Question

I need help please

Answer 1

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:

$\displaystyle\mathsf{Distance\:(D)= \sqrt{(x_2\:-x_1)^2\:+\:(y_2\:-y_1)^2}}$

Let (x₁, y₁) =   (1, 5)

     (x₂, y₂) =  (5, 2)

Step 1: Substitute points into the formula:  

$\displaystyle\mathsf{Distance\:(D)= \sqrt{(x_2\:-x_1)^2\:+\:(y_2\:-y_1)^2}}$

$\displaystyle\mathsf{Distance\:(D)= \sqrt{(5\:-1)^2\:+\:(2\:-5)^2}}$

Step 2: Subtract the integers in each of the parenthesis under the radical:

$\displaystyle\mathsf{Distance\:(D)= \sqrt{(4)^2\:+\:(-3)^2}}$

Step 3: Evaluate the powers (exponents):

$\displaystyle\mathsf{Distance\:(D)= \sqrt{16\:+\:9}}$

Step 4: Add 16 and 9:

$\displaystyle\mathsf{Distance\:(D)= \sqrt{25}}$

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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