Question

find the distance between the points. round to two decimal places if necessary.

Explanation:

Step1: Identify the points

The blue point is $(-2, 1)$, the black point is $(2, -11)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=-2,y_1=1,x_2=2,y_2=-11$:

$$ d=\sqrt{(2-(-2))^2+(-11-1)^2} $$

Step3: Simplify the differences

Calculate the terms inside the squares:

$$ d=\sqrt{(4)^2+(-12)^2} $$

Step4: Compute squared terms

Calculate the squares:

$$ d=\sqrt{16+144} $$

Step5: Sum and take square root

Add the terms and find the root:

$$ d=\sqrt{160}=4\sqrt{10}\approx12.65 $$

Answer:

12.65