Question

find the distance between (-1,3) and (2,7). d = √((x₁ - x₂)²+(y₁ - y₂)²) d = √((-1 - 2)²+(3 - 7)²) the distance is 5. √25 √9 + 16 √((-3)²+(-4)²) describe... drag the correct steps into the correct places and describe the steps.

Explanation:

Step1: Identify the coordinates

Let $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(2,7)$.

Step2: Substitute into distance - formula

$d = \sqrt{(x_1 - x_2)^2+(y_1 - y_2)^2}=\sqrt{(-1 - 2)^2+(3 - 7)^2}$.

Step3: Simplify the expressions inside the square - root

First, calculate $(-1 - 2)^2=(-3)^2 = 9$ and $(3 - 7)^2=(-4)^2 = 16$. Then $d=\sqrt{9 + 16}$.

Step4: Calculate the final result

Since $9+16 = 25$, then $d=\sqrt{25}=5$.

Answer:

The steps are:

1. Identify the coordinates: Let $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(2,7)$.
2. Substitute into distance - formula: $d = \sqrt{(-1 - 2)^2+(3 - 7)^2}$.
3. Simplify the expressions inside the square - root: $d=\sqrt{9 + 16}$.
4. Calculate the final result: $d = 5$.