Question

find the distance between (-3,5) and (-1, -4) using the distance formula.
√77
√7√85√14√22
√85
√14

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-3,5)\) and \((x_2,y_2)=(-1,-4)\)

Step2: Substitute into the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(-1-(-3))^2+(-4 - 5)^2}\)
Simplify inside the square - root:
\(x\) - difference: \(-1-(-3)=-1 + 3=2\)
\(y\) - difference: \(-4 - 5=-9\)
So \(d=\sqrt{2^2+(-9)^2}\)

Step3: Calculate the squares

\(2^2 = 4\) and \((-9)^2=81\)
Then \(d=\sqrt{4 + 81}\)

Step4: Add and simplify

\(4+81 = 85\), so \(d=\sqrt{85}\)

Answer:

\(\sqrt{85}\)