Question

calculating the distance between two points
what is the distance between the points $(-4,2)$ and $(3,-5)$?
$d = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
$\sqrt{10}$
$\sqrt{28}$
$\sqrt{98}$
$\sqrt{117}$

Explanation:

Step1: Substitute the coordinates into the distance formula

Let \((x_1,y_1)=(-4,2)\) and \((x_2,y_2)=(3,-5)\). Then \(x_2 - x_1=3-(-4)=3 + 4 = 7\) and \(y_2 - y_1=-5 - 2=-7\).

Step2: Calculate \((x_2 - x_1)^2+(y_2 - y_1)^2\)

\((x_2 - x_1)^2+(y_2 - y_1)^2=7^2+(-7)^2=49 + 49=98\).

Step3: Find the square - root

\(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{98}\).

Answer:

\(\sqrt{98}\)